61 lines
32 KiB
HTML
61 lines
32 KiB
HTML
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<meta name="viewport" content="width=device-width, initial-scale=1">
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<title>Machten</title>
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<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 8pt 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%}
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<body>
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<nav>
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<a href="/"><strong>Home</strong></a>
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<a href="/breuken">Breuken</a>
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<a href="/wortels">Wortels</a>
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<a href="/machten">Machten</a>
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</nav>
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<article>
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<h1 id="machten">Machten</h1>
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<h2 id="basisregels">Basisregels</h2>
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<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
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(x^{\textcolor{blue}{a}})^{\textcolor{red}{b}}
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=
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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>
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<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
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x^{\textcolor{blue}{a}}\cdot x^{\textcolor{red}{b}}
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=
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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>
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<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
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\frac{x^{\textcolor{blue}{a}}}{x^{\textcolor{red}{b}}}
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=
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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>
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<h2 id="machten-en-vermenigvuldigen">Machten en vermenigvuldigen</h2>
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<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
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\textcolor{blue}{a}^x\cdot\textcolor{red}{b}
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=
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\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>
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<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
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\textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{green}{c}
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=
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(\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>
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<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
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||
\textcolor{blue}{a}\cdot\textcolor{red}{b}^x\cdot\textcolor{red}{b}
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=
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||
\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>
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<h2 id="complexe-regels-voor-machten">Complexe regels voor machten</h2>
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<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
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\textcolor{blue}{a}x^{\textcolor{green}{n}}\cdot\textcolor{red}{b}x^{\textcolor{orange}{m}}
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=
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(\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>
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<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
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\textcolor{green}{n} \neq \textcolor{orange}{m} \Rightarrow \textcolor{blue}{a}x^{\textcolor{green}{n}}+\textcolor{red}{b}x^{\textcolor{orange}{m}}
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=
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\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>
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<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>
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