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Nevernown 2025-04-06 18:20:41 +02:00
parent f1bc884516
commit 382808ab2e
13 changed files with 487 additions and 10 deletions
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2
.astro/data-store.json
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[["Map",1,2],"meta::meta",["Map",3,4,5,6],"astro-version","5.5.6","astro-config-digest","{\"root\":{},\"srcDir\":{},\"publicDir\":{},\"outDir\":{},\"cacheDir\":{},\"site\":\"https://math.technotive.nl\",\"compressHTML\":false,\"base\":\"/\",\"trailingSlash\":\"ignore\",\"output\":\"static\",\"scopedStyleStrategy\":\"attribute\",\"build\":{\"format\":\"directory\",\"client\":{},\"server\":{},\"assets\":\"_astro\",\"serverEntry\":\"entry.mjs\",\"redirects\":true,\"inlineStylesheets\":\"auto\",\"concurrency\":1},\"server\":{\"open\":false,\"host\":false,\"port\":4321,\"streaming\":true,\"allowedHosts\":[]},\"redirects\":{},\"image\":{\"endpoint\":{\"route\":\"/_image\"},\"service\":{\"entrypoint\":\"astro/assets/services/sharp\",\"config\":{}},\"domains\":[],\"remotePatterns\":[]},\"devToolbar\":{\"enabled\":true},\"markdown\":{\"syntaxHighlight\":{\"type\":\"shiki\",\"excludeLangs\":[\"math\"]},\"shikiConfig\":{\"langs\":[],\"langAlias\":{},\"theme\":\"github-dark\",\"themes\":{},\"wrap\":false,\"transformers\":[]},\"remarkPlugins\":[],\"rehypePlugins\":[],\"remarkRehype\":{},\"gfm\":true,\"smartypants\":true},\"security\":{\"checkOrigin\":true},\"env\":{\"schema\":{},\"validateSecrets\":false},\"experimental\":{\"clientPrerender\":false,\"contentIntellisense\":false,\"responsiveImages\":false,\"serializeConfig\":false,\"headingIdCompat\":false,\"preserveScriptOrder\":false},\"legacy\":{\"collections\":false}}"] [["Map",1,2],"meta::meta",["Map",3,4,5,6],"astro-version","5.5.6","astro-config-digest","{\"root\":{},\"srcDir\":{},\"publicDir\":{},\"outDir\":{},\"cacheDir\":{},\"site\":\"https://math.technotive.nl\",\"compressHTML\":false,\"base\":\"/\",\"trailingSlash\":\"ignore\",\"output\":\"static\",\"scopedStyleStrategy\":\"attribute\",\"build\":{\"format\":\"directory\",\"client\":{},\"server\":{},\"assets\":\"_astro\",\"serverEntry\":\"entry.mjs\",\"redirects\":true,\"inlineStylesheets\":\"auto\",\"concurrency\":1},\"server\":{\"open\":false,\"host\":false,\"port\":4321,\"streaming\":true,\"allowedHosts\":[]},\"redirects\":{},\"image\":{\"endpoint\":{\"route\":\"/_image\"},\"service\":{\"entrypoint\":\"astro/assets/services/sharp\",\"config\":{}},\"domains\":[],\"remotePatterns\":[]},\"devToolbar\":{\"enabled\":true},\"markdown\":{\"syntaxHighlight\":{\"type\":\"shiki\",\"excludeLangs\":[\"math\"]},\"shikiConfig\":{\"langs\":[],\"langAlias\":{},\"theme\":\"github-dark\",\"themes\":{\"light\":\"min-light\",\"dark\":\"night-owl\"},\"wrap\":true,\"transformers\":[]},\"remarkPlugins\":[null],\"rehypePlugins\":[null],\"remarkRehype\":{},\"gfm\":true,\"smartypants\":true},\"security\":{\"checkOrigin\":true},\"env\":{\"schema\":{},\"validateSecrets\":false},\"experimental\":{\"clientPrerender\":false,\"contentIntellisense\":false,\"responsiveImages\":false,\"serializeConfig\":false,\"headingIdCompat\":false,\"preserveScriptOrder\":false},\"legacy\":{\"collections\":false}}"]

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astro.config.mjs
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import { defineConfig } from 'astro/config' import { defineConfig } from 'astro/config'
import remarkMath from "remark-math";
import rehypeKatex from "rehype-katex";
export default defineConfig({ export default defineConfig({
markdown: {
remarkPlugins: [remarkMath],
rehypePlugins: [rehypeKatex], // <- new plugin
shikiConfig: {
// For more themes, visit https://shiki.style/themes
themes: { light: "min-light", dark: "night-owl" },
wrap: true,
},
},
site: "https://math.technotive.nl", site: "https://math.technotive.nl",
trailingSlash: 'ignore', trailingSlash: 'ignore',
compressHTML: false compressHTML: false

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dist/breuken/index.html vendored Normal file
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dist/index.html vendored
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<head> <head>
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.css" integrity="sha384-zh0CIslj+VczCZtlzBcjt5ppRcsAmDnRem7ESsYwWwg3m/OaJ2l4x7YBZl9Kxxib" crossorigin="anonymous">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.js" integrity="sha384-Rma6DA2IPUwhNxmrB/7S3Tno0YY7sFu9WSYMCuulLhIqYSGZ2gKCJWIqhBWqMQfh" crossorigin="anonymous"></script>
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/contrib/auto-render.min.js" integrity="sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<title>Home</title> <title>Home</title>
<style>*{margin:0;padding:0}body{display:flex;flex-direction:row;font-family:Courier New,Courier,monospace}nav{padding-top:12pt;display:flex;flex-direction:column;background-color:#4682b4;min-width:120pt;height:100vh}nav a{padding:0 4pt 2pt;display:inline-block;font-size:large;color:#f5f5f5}nav a:hover{background-image:linear-gradient(to bottom,#4682b4,#191970)}article{padding-top:12pt;padding-left:12pt} <style>*{margin:0;padding:0}h1{font-size:24pt;margin-bottom:8pt}h2{font-size:18pt;margin-bottom:8pt}h3{font-size:16pt;margin-bottom:8pt}p{margin-bottom:12pt}body{display:flex;flex-direction:row;font-family:Courier New,Courier,monospace}nav{padding-top:12pt;display:flex;flex-direction:column;background-color:#4682b4;min-width:120pt;height:100vh}nav a{padding:0 4pt 2pt 18pt;display:inline-block;font-size:large;color:#f5f5f5}nav a:hover{background-image:linear-gradient(to bottom,#4682b4,#191970)}article{padding-top:12pt;padding-left:12pt;width:100%}
</style></head> </style></head>
<body> <body>
<nav> <nav>
<a href="/">Home</a> <a href="/">Home</a>
<a href="#">Breuken</a> <a href="/breuken">Breuken</a>
<a href="#">Machten</a> <a href="/wortels">Wortels</a>
<a href="/machten">Machten</a>
</nav> </nav>
<article> <article>
<h1 id="wiskunde">Wiskunde</h1> <!-- your content is injected here --> <h1 id="wiskunde">Wiskunde</h1>
<p>Links vind je uitleg van basisconcepten die je nodig hebt binnen de wiskunde. Gebruik dit tijdens het leren om je basisvaardigheden na te lopen.</p>
<p>Hieronder vind je nog een aantal korte opmeringen die niet onder de onderwerpen in het linker-menu vallen.</p>
<h2 id="haakjes">Haakjes</h2>
<p>Haakjes gaan altijd voor met uitwerken, maar soms moet je de inhoud loswerken:</p>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo stretchy="false">(</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>+</mo><mstyle mathcolor="green"><mi>c</mi></mstyle><mo stretchy="false">)</mo><mo>=</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>+</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="green"><mi>c</mi></mstyle></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{blue}{a}(\textcolor{red}{b}+\textcolor{green}{c})
= \textcolor{blue}{a}\cdot\textcolor{red}{b}+\textcolor{blue}{a}\cdot\textcolor{green}{c}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mopen sizing reset-size6 size8">(</span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span><span class="mclose sizing reset-size6 size8">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.12em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.62em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mo stretchy="false">(</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>+</mo><mstyle mathcolor="orange"><mi>d</mi></mstyle><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>+</mo><mstyle mathcolor="green"><mi>c</mi></mstyle><mo stretchy="false">)</mo><mo>=</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>+</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="green"><mi>c</mi></mstyle><mo>+</mo><mstyle mathcolor="orange"><mi>d</mi></mstyle><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>+</mo><mstyle mathcolor="orange"><mi>d</mi></mstyle><mo>⋅</mo><mstyle mathcolor="green"><mi>c</mi></mstyle></mstyle></mrow><annotation encoding="application/x-tex">\Large
(\textcolor{blue}{a}+\textcolor{orange}{d})(\textcolor{red}{b}+\textcolor{green}{c})
=
\textcolor{blue}{a}\cdot\textcolor{red}{b}+\textcolor{blue}{a}\cdot\textcolor{green}{c}+\textcolor{orange}{d}\cdot\textcolor{red}{b}+\textcolor{orange}{d}\cdot\textcolor{green}{c}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mopen sizing reset-size6 size8">(</span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:orange;">d</span><span class="mclose sizing reset-size6 size8">)</span><span class="mopen sizing reset-size6 size8">(</span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span><span class="mclose sizing reset-size6 size8">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.12em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.96em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:orange;">d</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.12em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:orange;">d</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.62em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span></span></span></span></span> <!-- your content is injected here -->
</article> </article>
</body></html> </body></html>

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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.css" integrity="sha384-zh0CIslj+VczCZtlzBcjt5ppRcsAmDnRem7ESsYwWwg3m/OaJ2l4x7YBZl9Kxxib" crossorigin="anonymous">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.js" integrity="sha384-Rma6DA2IPUwhNxmrB/7S3Tno0YY7sFu9WSYMCuulLhIqYSGZ2gKCJWIqhBWqMQfh" crossorigin="anonymous"></script>
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/contrib/auto-render.min.js" integrity="sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh" crossorigin="anonymous" onload="renderMathInElement(document.body);"></script>
<title>Machten</title>
<style>*{margin:0;padding:0}h1{font-size:24pt;margin-bottom:8pt}h2{font-size:18pt;margin-bottom:8pt}h3{font-size:16pt;margin-bottom:8pt}p{margin-bottom:12pt}body{display:flex;flex-direction:row;font-family:Courier New,Courier,monospace}nav{padding-top:12pt;display:flex;flex-direction:column;background-color:#4682b4;min-width:120pt;height:100vh}nav a{padding:0 4pt 2pt 18pt;display:inline-block;font-size:large;color:#f5f5f5}nav a:hover{background-image:linear-gradient(to bottom,#4682b4,#191970)}article{padding-top:12pt;padding-left:12pt;width:100%}
</style></head>
<body>
<nav>
<a href="/">Home</a>
<a href="/breuken">Breuken</a>
<a href="/wortels">Wortels</a>
<a href="/machten">Machten</a>
</nav>
<article>
<h1 id="machten">Machten</h1>
<h2 id="basisregels">Basisregels</h2>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mo stretchy="false">(</mo><msup><mi>x</mi><mstyle mathcolor="blue"><mi>a</mi></mstyle></msup><msup><mo stretchy="false">)</mo><mstyle mathcolor="red"><mi>b</mi></mstyle></msup><mo>=</mo><msup><mi>x</mi><mrow><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
(x^{\textcolor{blue}{a}})^{\textcolor{red}{b}}
=
x^{\textcolor{blue}{a}\cdot\textcolor{red}{b}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.6492em;vertical-align:-0.36em;"></span><span class="mopen sizing reset-size6 size8">(</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">a</span></span></span></span></span></span></span></span></span><span class="mclose sizing reset-size6 size8"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8952em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:red;">b</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2892em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8952em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">a</span><span class="mbin mtight">⋅</span><span class="mord mathnormal mtight" style="color:red;">b</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><msup><mi>x</mi><mstyle mathcolor="blue"><mi>a</mi></mstyle></msup><mo>⋅</mo><msup><mi>x</mi><mstyle mathcolor="red"><mi>b</mi></mstyle></msup><mo>=</mo><msup><mi>x</mi><mrow><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>+</mo><mstyle mathcolor="red"><mi>b</mi></mstyle></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
x^{\textcolor{blue}{a}}\cdot x^{\textcolor{red}{b}}
=
x^{\textcolor{blue}{a}+\textcolor{red}{b}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">a</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2892em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8952em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:red;">b</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2892em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8952em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">a</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="color:red;">b</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mfrac><msup><mi>x</mi><mstyle mathcolor="blue"><mi>a</mi></mstyle></msup><msup><mi>x</mi><mstyle mathcolor="red"><mi>b</mi></mstyle></msup></mfrac><mo>=</mo><msup><mi>x</mi><mrow><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>−</mo><mstyle mathcolor="red"><mi>b</mi></mstyle></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\frac{x^{\textcolor{blue}{a}}}{x^{\textcolor{red}{b}}}
=
x^{\textcolor{blue}{a}-\textcolor{red}{b}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.916em;vertical-align:-0.9878em;"></span><span class="mord sizing reset-size6 size8"><span class="mopen nulldelimiter sizing reset-size8 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.339em;"><span style="top:-2.754em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7712em;"><span style="top:-3.289em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:red;">b</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.67em;"><span class="pstrut" style="height:3.44em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.117em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.662em;"><span style="top:-3.363em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">a</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size8 size6"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2892em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8952em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">a</span><span class="mbin mtight">−</span><span class="mord mathnormal mtight" style="color:red;">b</span></span></span></span></span></span></span></span></span></span></span></span></span>
<h2 id="machten-en-vermenigvuldigen">Machten en vermenigvuldigen</h2>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><msup><mstyle mathcolor="blue"><mi>a</mi></mstyle><mi>x</mi></msup><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>=</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>⋅</mo><msup><mstyle mathcolor="blue"><mi>a</mi></mstyle><mi>x</mi></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{blue}{a}^x\cdot\textcolor{red}{b}
=
\textcolor{red}{b}\cdot\textcolor{blue}{a}^x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal" style="color:blue;">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal" style="color:blue;">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><msup><mstyle mathcolor="red"><mi>b</mi></mstyle><mi>x</mi></msup><mo>⋅</mo><mstyle mathcolor="green"><mi>c</mi></mstyle><mo>=</mo><mo stretchy="false">(</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="green"><mi>c</mi></mstyle><mo stretchy="false">)</mo><mo>⋅</mo><msup><mstyle mathcolor="red"><mi>b</mi></mstyle><mi>x</mi></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{green}{c}
=
(\textcolor{blue}{a}\cdot \textcolor{green}{c})\cdot\textcolor{red}{b}^{x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal" style="color:red;">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.62em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mopen sizing reset-size6 size8">(</span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">c</span><span class="mclose sizing reset-size6 size8">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal" style="color:red;">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><msup><mstyle mathcolor="red"><mi>b</mi></mstyle><mi>x</mi></msup><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo>=</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><msup><mstyle mathcolor="red"><mi>b</mi></mstyle><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{red}{b}
=
\textcolor{blue}{a}\cdot\textcolor{red}{b}^{x+1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal" style="color:red;">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mathnormal mtight">x</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.64em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2392em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal" style="color:red;">b</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8605em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span>
<h2 id="complexe-regels-voor-machten">Complexe regels voor machten</h2>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mstyle mathcolor="blue"><mi>a</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="green"><mi>n</mi></mstyle></msup><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="orange"><mi>m</mi></mstyle></msup><mo>=</mo><mo stretchy="false">(</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo stretchy="false">)</mo><msup><mi>x</mi><mrow><mstyle mathcolor="green"><mi>n</mi></mstyle><mo>+</mo><mstyle mathcolor="orange"><mi>m</mi></mstyle></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{blue}{a}x^{\textcolor{green}{n}}\cdot\textcolor{red}{b}x^{\textcolor{orange}{m}}
=
(\textcolor{blue}{a}\cdot \textcolor{red}{b})x^{\textcolor{green}{n}+\textcolor{orange}{m}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:orange;">m</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mopen sizing reset-size6 size8">(</span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.5381em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mclose sizing reset-size6 size8">)</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8181em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span><span class="mbin mtight">+</span><span class="mord mathnormal mtight" style="color:orange;">m</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mstyle mathcolor="green"><mi>n</mi></mstyle><mo mathvariant="normal">≠</mo><mstyle mathcolor="orange"><mi>m</mi></mstyle><mo>⇒</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="green"><mi>n</mi></mstyle></msup><mo>+</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="orange"><mi>m</mi></mstyle></msup><mo>=</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="green"><mi>n</mi></mstyle></msup><mo>+</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="orange"><mi>m</mi></mstyle></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{green}{n} \neq \textcolor{orange}{m} \Rightarrow \textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}}
=
\textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.28em;vertical-align:-0.28em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:green;">n</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.62em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:orange;">m</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">⇒</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1453em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:orange;">m</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1453em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:orange;">m</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mstyle mathcolor="blue"><mi>a</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="green"><mi>n</mi></mstyle></msup><mo>+</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><msup><mi>x</mi><mstyle mathcolor="green"><mi>n</mi></mstyle></msup><mo>=</mo><mo stretchy="false">(</mo><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>+</mo><mstyle mathcolor="red"><mi>b</mi></mstyle><mo stretchy="false">)</mo><msup><mi>x</mi><mstyle mathcolor="green"><mi>n</mi></mstyle></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{green}{n}}
=
(\textcolor{blue}{a}+\textcolor{red}{b})x^{\textcolor{green}{n}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1453em;vertical-align:-0.12em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0253em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mopen sizing reset-size6 size8">(</span><span class="mord mathnormal sizing reset-size6 size8" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.44em;vertical-align:-0.36em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="color:red;">b</span><span class="mclose sizing reset-size6 size8">)</span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:green;">n</span></span></span></span></span></span></span></span></span></span></span></span></span> <!-- your content is injected here -->
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<article>
<h1 id="wortels">Wortels</h1>
<h2 id="vermenigvuldiging">Vermenigvuldiging</h2>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><msqrt><mrow><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mstyle mathcolor="red"><mi>b</mi></mstyle></mrow></msqrt><mo>=</mo><msqrt><mstyle mathcolor="blue"><mi>a</mi></mstyle></msqrt><mo>⋅</mo><msqrt><mstyle mathcolor="red"><mi>b</mi></mstyle></msqrt></mstyle></mrow><annotation encoding="application/x-tex">\Large
\sqrt{\textcolor{blue}{a}\cdot\textcolor{red}{b}}
=
\sqrt{\textcolor{blue}{a}}\cdot\sqrt{\textcolor{red}{b}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4976em;vertical-align:-0.0848em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9811em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="color:red;">b</span></span></span><span style="top:-3.3811em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.0589em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4976em;vertical-align:-0.2748em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8492em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="color:blue;">a</span></span></span><span style="top:-3.2492em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1908em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.4976em;vertical-align:-0.0848em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9811em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="color:red;">b</span></span></span><span style="top:-3.3811em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
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H400000v40H845.2724
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M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.0589em;"><span></span></span></span></span></span></span></span></span></span>
<h2 id="vermenigvuldigen-met-breuken">Vermenigvuldigen met breuken</h2>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><msqrt><mfrac><mstyle mathcolor="blue"><mi>a</mi></mstyle><mstyle mathcolor="red"><mi>b</mi></mstyle></mfrac></msqrt><mo>=</mo><msqrt><mrow><mstyle mathcolor="blue"><mi>a</mi></mstyle><mo>⋅</mo><mfrac><mn>1</mn><mstyle mathcolor="red"><mi>b</mi></mstyle></mfrac></mrow></msqrt><mo>=</mo><msqrt><mstyle mathcolor="blue"><mi>a</mi></mstyle></msqrt><mo>⋅</mo><msqrt><mfrac><mn>1</mn><mstyle mathcolor="red"><mi>b</mi></mstyle></mfrac></msqrt></mstyle></mrow><annotation encoding="application/x-tex">\Large
\sqrt{\frac{\textcolor{blue}{a}}{\textcolor{red}{b}}}
=
\sqrt{\textcolor{blue}{a}\cdot\frac{1}{\textcolor{red}{b}}}
=
\sqrt{\textcolor{blue}{a}}\cdot\sqrt{\frac{1}{\textcolor{red}{b}}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.5136em;vertical-align:-1.2893em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5447em;"><span class="svg-align" style="top:-4.4em;"><span class="pstrut" style="height:4.4em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mopen nulldelimiter sizing reset-size8 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.754em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord mathnormal" style="color:red;">b</span></span></span><span style="top:-3.67em;"><span class="pstrut" style="height:3.44em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.117em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord mathnormal" style="color:blue;">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size8 size6"></span></span></span></span><span style="top:-3.5047em;"><span class="pstrut" style="height:4.4em;"></span><span class="hide-tail" style="min-width:1.02em;height:2.48em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="2.48em" viewBox="0 0 400000 2592" preserveAspectRatio="xMinYMin slice"><path d="M424,2478
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h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8953em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3.5136em;vertical-align:-1.1353em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6516em;"><span class="svg-align" style="top:-4.4em;"><span class="pstrut" style="height:4.4em;"></span><span class="mord" style="padding-left:1em;"><span class="mord mathnormal" style="color:blue;">a</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter sizing reset-size8 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.754em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord mathnormal" style="color:red;">b</span></span></span><span style="top:-3.67em;"><span class="pstrut" style="height:3.44em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.117em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size8 size6"></span></span></span></span><span style="top:-3.6116em;"><span class="pstrut" style="height:4.4em;"></span><span class="hide-tail" style="min-width:1.02em;height:2.48em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="2.48em" viewBox="0 0 400000 2592" preserveAspectRatio="xMinYMin slice"><path d="M424,2478
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s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121
s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
l0 -0c4,-6.7,10,-10,18,-10 H400000
v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7884em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.4976em;vertical-align:-0.2748em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8492em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal" style="color:blue;">a</span></span></span><span style="top:-3.2492em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
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c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
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c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1908em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin sizing reset-size6 size8">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:3.5136em;vertical-align:-1.1353em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6516em;"><span class="svg-align" style="top:-4.4em;"><span class="pstrut" style="height:4.4em;"></span><span class="mord" style="padding-left:1em;"><span class="mord"><span class="mopen nulldelimiter sizing reset-size8 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.754em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord mathnormal" style="color:red;">b</span></span></span><span style="top:-3.67em;"><span class="pstrut" style="height:3.44em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.117em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size8 size6"></span></span></span></span><span style="top:-3.6116em;"><span class="pstrut" style="height:4.4em;"></span><span class="hide-tail" style="min-width:1.02em;height:2.48em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="2.48em" viewBox="0 0 400000 2592" preserveAspectRatio="xMinYMin slice"><path d="M424,2478
c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20
s-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121
s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
l0 -0c4,-6.7,10,-10,18,-10 H400000
v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7884em;"><span></span></span></span></span></span></span></span></span></span>
<h2 id="herschrijven-als-macht">Herschrijven als Macht</h2>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><msqrt><mo stretchy="false">(</mo></msqrt><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\sqrt(x) = x^{1/2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.7856em;vertical-align:-0.3688em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9839em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mopen" style="padding-left:1em;">(</span></span><span style="top:-3.1839em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2561em;"><span></span></span></span></span></span><span class="mord mathnormal sizing reset-size6 size8">x</span><span class="mclose sizing reset-size6 size8">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3447em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9338em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mtight">1/2</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mroot><mo stretchy="false" lspace="0em" rspace="0em">(</mo><mn>3</mn></mroot><msup><mi>x</mi><mn>2</mn></msup><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mi mathvariant="normal">/</mi><mn>3</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\sqrt[3](x^2)=x^{2/3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.7856em;vertical-align:-0.3688em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="root"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7499em;"><span style="top:-3.1367em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size8 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9839em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord" style="padding-left:1em;"><span class="mopen">(</span></span></span><span style="top:-3.1839em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2561em;"><span></span></span></span></span></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8605em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose sizing reset-size6 size8">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3447em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9338em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mtight">2/3</span></span></span></span></span></span></span></span></span></span></span></span></span>
<span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mroot><mo stretchy="false" lspace="0em" rspace="0em">(</mo><mstyle mathcolor="blue"><mi>n</mi></mstyle></mroot><msup><mi>x</mi><mstyle mathcolor="red"><mi>m</mi></mstyle></msup><mo stretchy="false">)</mo><mo>=</mo><msup><mi>x</mi><mrow><mstyle mathcolor="red"><mi>m</mi></mstyle><mi mathvariant="normal">/</mi><mstyle mathcolor="blue"><mi>n</mi></mstyle></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\Large
\sqrt[\textcolor{blue}{n}](x^{\textcolor{red}{m}})
=
x^{\textcolor{red}{m}/\textcolor{blue}{n}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.7856em;vertical-align:-0.3688em;"></span><span class="mord sqrt sizing reset-size6 size8"><span class="root"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.646em;"><span style="top:-3.1367em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size8 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:blue;">n</span></span></span></span></span></span></span></span><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9839em;"><span class="svg-align" style="top:-3.44em;"><span class="pstrut" style="height:3.44em;"></span><span class="mord" style="padding-left:1em;"><span class="mopen">(</span></span></span><span style="top:-3.1839em;"><span class="pstrut" style="height:3.44em;"></span><span class="hide-tail" style="min-width:1.02em;height:1.28em;"><svg xmlns="http://www.w3.org/2000/svg" width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z"></path></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2561em;"><span></span></span></span></span></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.712em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:red;">m</span></span></span></span></span></span></span></span></span><span class="mclose sizing reset-size6 size8">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel sizing reset-size6 size8">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3447em;"></span><span class="mord sizing reset-size6 size8"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9338em;"><span style="top:-3.413em;margin-right:0.0347em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size8 size6 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="color:red;">m</span><span class="mord mtight">/</span><span class="mord mathnormal mtight" style="color:blue;">n</span></span></span></span></span></span></span></span></span></span></span></span></span> <!-- your content is injected here -->
</article>
</body></html>

5
package.json
View File

@ -16,6 +16,9 @@
"author": "", "author": "",
"license": "ISC", "license": "ISC",
"dependencies": { "dependencies": {
"astro": "^5.5.6" "astro": "^5.5.6",
"katex": "^0.16.21",
"rehype-katex": "^7.0.1",
"remark-math": "^6.0.0"
} }
} }

19
src/css/math.css
View File

@ -1,7 +1,23 @@
* { * {
margin: 0; margin: 0;
padding: 0; padding: 0;
}
h1 {
font-size: 24pt;
margin-bottom: 8pt;
}
h2 {
font-size: 18pt;
margin-bottom: 8pt;
}
h3 {
font-size: 16pt;
margin-bottom: 8pt;
}
p {
margin-bottom: 12pt;
} }
body { body {
@ -19,7 +35,7 @@ nav {
height: 100vh; height: 100vh;
} }
nav a { nav a {
padding: 0pt 4pt 2pt 4pt; padding: 0pt 4pt 2pt 18pt;
display: inline-block; display: inline-block;
font-size: large; font-size: large;
color: whitesmoke; color: whitesmoke;
@ -32,4 +48,5 @@ nav a:hover {
article { article {
padding-top: 12pt; padding-top: 12pt;
padding-left: 12pt; padding-left: 12pt;
width: 100%;
} }

10
src/layout/math.astro
View File

@ -2,17 +2,23 @@
import '../css/math.css'; import '../css/math.css';
const { frontmatter } = Astro.props; const { frontmatter } = Astro.props;
--- ---
<!DOCTYPE html>
<html lang="en"> <html lang="en">
<head> <head>
<meta charset="utf-8"> <meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1"> <meta name="viewport" content="width=device-width, initial-scale=1">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.css" integrity="sha384-zh0CIslj+VczCZtlzBcjt5ppRcsAmDnRem7ESsYwWwg3m/OaJ2l4x7YBZl9Kxxib" crossorigin="anonymous">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/katex.min.js" integrity="sha384-Rma6DA2IPUwhNxmrB/7S3Tno0YY7sFu9WSYMCuulLhIqYSGZ2gKCJWIqhBWqMQfh" crossorigin="anonymous"></script>
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.21/dist/contrib/auto-render.min.js" integrity="sha384-hCXGrW6PitJEwbkoStFjeJxv+fSOOQKOPbJxSfM6G5sWZjAyWhXiTIIAmQqnlLlh" crossorigin="anonymous"
onload="renderMathInElement(document.body);"></script>
<title>{frontmatter.title}</title> <title>{frontmatter.title}</title>
</head> </head>
<body> <body>
<nav> <nav>
<a href="/">Home</a> <a href="/">Home</a>
<a href="#">Breuken</a> <a href="/breuken">Breuken</a>
<a href="#">Machten</a> <a href="/wortels">Wortels</a>
<a href="/machten">Machten</a>
</nav> </nav>
<article> <article>
<slot /> <!-- your content is injected here --> <slot /> <!-- your content is injected here -->

41
src/pages/breuken.md Normal file
View File

@ -0,0 +1,41 @@
---
layout: "../layout/math.astro"
title: "Breuken"
---
# Breuken
## Vermenigvuldigen
$$
\Large
\frac{\textcolor{blue}{a}}{\textcolor{red}{b}}
\cdot
\frac{\textcolor{green}{c}}{\textcolor{orange}{d}}
=
\frac{\textcolor{blue}{a}\cdot \textcolor{green}{c}}{\textcolor{red}{b}\cdot \textcolor{orange}{d}}
$$
## Optellen
$$
\Large
\frac{\textcolor{blue}{a}}{\textcolor{red}{b}}+\frac{\textcolor{green}{c}}{\textcolor{orange}{d}}
=
\frac{(\textcolor{blue}{a}\cdot \textcolor{orange}{d})+(\textcolor{green}{c}\cdot \textcolor{red}{b})}{\textcolor{red}{b}\cdot \textcolor{orange}{d}}
$$
$$
\Large
x\frac{\textcolor{blue}{a}}{\textcolor{red}{b}}+y\frac{\textcolor{green}{c}}{\textcolor{orange}{d}}
=
x+y+\frac{\textcolor{blue}{a}}{\textcolor{red}{b}}+\frac{\textcolor{green}{c}}{\textcolor{orange}{d}}
$$
## Delen
$$
\Large
\frac{\textcolor{blue}{a}}{(\frac{\textcolor{red}{b}}{\textcolor{green}{c}})}
=
\textcolor{blue}{a}\cdot\frac{\textcolor{green}{c}}{\textcolor{red}{b}}
$$
$$
\Large
\frac{(\frac{\textcolor{blue}{a}}{\textcolor{red}{b}})}{\textcolor{green}{c}}
=
\frac{\textcolor{blue}{a}}{\textcolor{red}{b}\cdot \textcolor{green}{c}}
$$

20
src/pages/index.md
View File

@ -2,4 +2,22 @@
layout: "../layout/math.astro" layout: "../layout/math.astro"
title: "Home" title: "Home"
--- ---
# Wiskunde # Wiskunde
Links vind je uitleg van basisconcepten die je nodig hebt binnen de wiskunde. Gebruik dit tijdens het leren om je basisvaardigheden na te lopen.
Hieronder vind je nog een aantal korte opmeringen die niet onder de onderwerpen in het linker-menu vallen.
## Haakjes
Haakjes gaan altijd voor met uitwerken, maar soms moet je de inhoud loswerken:
$$
\Large
\textcolor{blue}{a}(\textcolor{red}{b}+\textcolor{green}{c})
= \textcolor{blue}{a}\cdot\textcolor{red}{b}+\textcolor{blue}{a}\cdot\textcolor{green}{c}
$$
$$
\Large
(\textcolor{blue}{a}+\textcolor{orange}{d})(\textcolor{red}{b}+\textcolor{green}{c})
=
\textcolor{blue}{a}\cdot\textcolor{red}{b}+\textcolor{blue}{a}\cdot\textcolor{green}{c}+\textcolor{orange}{d}\cdot\textcolor{red}{b}+\textcolor{orange}{d}\cdot\textcolor{green}{c}
$$

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---
layout: "../layout/math.astro"
title: "Machten"
---
# Machten
## Basisregels
$$
\Large
(x^{\textcolor{blue}{a}})^{\textcolor{red}{b}}
=
x^{\textcolor{blue}{a}\cdot\textcolor{red}{b}}
$$
$$
\Large
x^{\textcolor{blue}{a}}\cdot x^{\textcolor{red}{b}}
=
x^{\textcolor{blue}{a}+\textcolor{red}{b}}
$$
$$
\Large
\frac{x^{\textcolor{blue}{a}}}{x^{\textcolor{red}{b}}}
=
x^{\textcolor{blue}{a}-\textcolor{red}{b}}
$$
## Machten en vermenigvuldigen
$$
\Large
\textcolor{blue}{a}^x\cdot\textcolor{red}{b}
=
\textcolor{red}{b}\cdot\textcolor{blue}{a}^x
$$
$$
\Large
\textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{green}{c}
=
(\textcolor{blue}{a}\cdot \textcolor{green}{c})\cdot\textcolor{red}{b}^{x}
$$
$$
\Large
\textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{red}{b}
=
\textcolor{blue}{a}\cdot\textcolor{red}{b}^{x+1}
$$
## Complexe regels voor machten
$$
\Large
\textcolor{blue}{a}x^{\textcolor{green}{n}}\cdot\textcolor{red}{b}x^{\textcolor{orange}{m}}
=
(\textcolor{blue}{a}\cdot \textcolor{red}{b})x^{\textcolor{green}{n}+\textcolor{orange}{m}}
$$
$$
\Large
\textcolor{green}{n} \neq \textcolor{orange}{m} \Rightarrow \textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}}
=
\textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}}
$$
$$
\Large
\textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{green}{n}}
=
(\textcolor{blue}{a}+\textcolor{red}{b})x^{\textcolor{green}{n}}
$$

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---
layout: "../layout/math.astro"
title: "Wortels"
---
# Wortels
## Vermenigvuldiging
$$
\Large
\sqrt{\textcolor{blue}{a}\cdot\textcolor{red}{b}}
=
\sqrt{\textcolor{blue}{a}}\cdot\sqrt{\textcolor{red}{b}}
$$
## Vermenigvuldigen met breuken
$$
\Large
\sqrt{\frac{\textcolor{blue}{a}}{\textcolor{red}{b}}}
=
\sqrt{\textcolor{blue}{a}\cdot\frac{1}{\textcolor{red}{b}}}
=
\sqrt{\textcolor{blue}{a}}\cdot\sqrt{\frac{1}{\textcolor{red}{b}}}
$$
## Herschrijven als Macht
$$
\Large
\sqrt(x) = x^{1/2}
$$
$$
\Large
\sqrt[3](x^2)=x^{2/3}
$$
$$
\Large
\sqrt[\textcolor{blue}{n}](x^{\textcolor{red}{m}})
=
x^{\textcolor{red}{m}/\textcolor{blue}{n}}
$$