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<h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3>
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<h4>Table of Contents</h4>
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<h1 class="banner-text" id="banner-txt">Exponents</h1>
<h3 class="banner-text" id="banner-txt">Chapter 1</h3>
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<section>
<h1 id="exponent">Exponents</h1>
x<sup>n</sup> = x<sub>1</sub> × x<sub>2</sub> × ... × x<sub>n</sub>
<h2 id="exponent--examples">Examples</h2>
<ul>
<li>2<sup>5</sup> = 2 × 2 × 2 × 2 × 2 = 32</li>
<li>5<sup>7</sup> = 5 × 5 × 5 × 5 × 5 × 5 × 5 = 78.125</li>
</ul>
<h1 id="exponent-operations">Exponent Operations</h1>
<h2 id="exponent-operations--multiplication">Multiplication</h2>
a<sup>x</sup> × b<sup>y</sup> = (a × b)<sup>x + y</sup>
<ul>
<li>10<sup>4</sup> × 2<sup>2</sup> = (10 × 2)<sup>4 + 2</sup> = <strong>20<sup>6</sup></strong></li>
</ul>
<h2 id="exponent-operations--division">Division</h2>
a<sup>x</sup> ÷ b<sup>y</sup> = (a ÷ b)<sup>x - y</sup>
<ul>
<li>10<sup>3</sup> ÷ 2<sup>4</sup> = (10 ÷ 2)<sup>4 - 2</sup> = <strong>5<sup>2</sup></strong></li>
</ul>
<h2 id="exponent-operations--exponent">Exponent</h2>
(a<sup>x</sup>)<sup>y</sup> = a<sup>x × y</sup>
<ul>
<li>(2<sup>2</sup>)<sup>3</sup> = 2<sup>2 × 3</sup> <strong>= 2<sup>6</sup> = 64</li></strong>
</ul>
<h1 id="zero-exponent">Zero Exponent</h1>
<p>a<sup>0</sup> = 1</p>
<h2 id="zero-exponent--examples">Examples</h2>
<ul>
<li>5<sup>0</sup> = 1</li>
<li>7<sup>0</sup> = 1</li>
<li>100<sup>0</sup> = 1</li>
<li>28,67<sup>0</sup> = 1</li>
</ul>
<h1 id="one-exponent">One Exponent</h1>
<p>a<sup>1</sup> = a</p>
<h2 id="one-exponent--examples">Examples</h2>
<ul>
<li>5<sup>1</sup> = 5</li>
<li>7<sup>1</sup> = 7</li>
<li>100<sup>1</sup> = 100</li>
<li>28,67<sup>1</sup> = 28,67</li>
</ul>
<h1 id="fractional-exponent">Fractional Exponent</h1>
<img src="/assets/images/math/fractional_exponent.svg" alt="">
<p>x <sup><span class="frac"><sup>y</sup><span>⁄</span><sub>z</sub></span></sup> =
<sup>z</sup><span><span class="root">x</span><sup style="font-size: small;">y</sup><span></span></span></p>
<h2 id="fractional-exponent--examples">Examples</h2>
<ul>
<li>5 <sup><span class="frac"><sup>1</sup><span>⁄</span><sub>2</sub></span></sup> =
<sup>2</sup><span><span class="root">5</span></span></li>
<li>7 <sup><span class="frac"><sup>2</sup><span>⁄</span><sub>3</sub></span></sup> =
<sup>3</sup><span><span class="root">7<sup>2</sup></span></span></li>
</ul>
<p><strong>Small Note:</strong> 2</sup><span class="root">x</span> or <span class="root">x</span> menans square root. The 2 before root should be removed. The 2 is only present for easier purposes.<br>3</sup><span><span class="root">x</span> means cubic root.</p>
<h1 id="exponential-equation">Exponential Equation</h1>
<ol>
<li>2<sup>x + 5</sup> = 64<br>
= <span style="text-decoration: line-through;">2</span><sup>x + 5</sup> = <span style="text-decoration: line-through;">2</span><sup>6</sup> <sub>↖ ubah ke bentuk 2 berpangkat (2<sup>x</sup>)</sub><br>
= x + 5 = 6<br>
= x = <strong>1</strong>
</li>
<li>16<sup>x + 2</sup> = 32<br>
= (2<sup>4</sup>)<sup>x + 2</sup> = 2<sup>5</sup><br>
= <span style="text-decoration: line-through;">2</span><sup>4x + 8</sup> = <span style="text-decoration: line-through;">2</span><sup>5</sup><br>
= 4x + 8 = 5<br>
= 4x = 5 - 8<br>
= 4x = -3<br>
= x = <span class="frac"><sup>-3</sup><span>⁄</span><sub>4</sub></span> = <strong>-<span class="frac"><sup>3</sup><span>⁄</span><sub>4</sub></span></strong>
</li>
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