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<title>Wortels</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%}
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<a href="/">Home</a>
<a href="/breuken">Breuken</a>
<a href="/wortels">Wortels</a>
<a href="/machten">Machten</a>
</nav>
<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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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:0.0589em;"><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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s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
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H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
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: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
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
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:0.0589em;"><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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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:0.8953em;"><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
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l0 -0c4,-6.7,10,-10,18,-10 H400000
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c-2,6,-10,9,-24,9
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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:0.7884em;"><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
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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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
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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
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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
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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"><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
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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 -->
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