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-<!DOCTYPE html>
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- <title>Al Azhar 9th Grade Lesson Notes</title>
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- <h3 id="title" class="align-center">Al Azhar 9th Grade Lesson Notes</h3>
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-
- <div>
- <a href="/about/author.html" class="sidebar-link link">About the Author</a>
- <a href="/about/school.html" class="sidebar-link link">About School</a>
- <a href="/lessons" class="sidebar-link link">Lessons</a>
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- <div id="toc">
- <h4>Table of Contents</h4>
- </div>
- </div>
- </div>
-
- <div class="banner-container" id="banner">
- <div class="banner-bg" id="img-supplies"></div>
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- <div class="banner-text-container">
- <h1 class="banner-text" id="banner-txt">Exponents</h1>
- <h3 class="banner-text" id="banner-txt">Chapter 1</h3>
- </div>
- </div>
-
- <div class="chip-container" id="chip-container">
- <div class="chip"><span>✅ Verified</span></div>
- </div>
-
- <div id="main">
- <section>
- <h1 id="exponent">Exponents</h1>
- x<sup>n</sup> = x<sub>1</sub> &times; x<sub>2</sub> &times; ... &times; x<sub>n</sub>
- <h2 id="exponent--examples">Examples</h2>
- <ul>
- <li>2<sup>5</sup> = 2 &times; 2 &times; 2 &times; 2 &times; 2 = 32</li>
- <li>5<sup>7</sup> = 5 &times; 5 &times; 5 &times; 5 &times; 5 &times; 5 &times; 5 = 78.125</li>
- </ul>
- <h1 id="exponent-operations">Exponent Operations</h1>
- <h2 id="exponent-operations--multiplication">Multiplication</h2>
- a<sup>x</sup> &times; b<sup>y</sup> = (a &times; b)<sup>x + y</sup>
- <ul>
- <li>10<sup>4</sup> &times; 2<sup>2</sup> = (10 &times; 2)<sup>4 + 2</sup> = <strong>20<sup>6</sup></strong></li>
- </ul>
- <h2 id="exponent-operations--division">Division</h2>
- a<sup>x</sup> &divide; b<sup>y</sup> = (a &divide; b)<sup>x - y</sup>
- <ul>
- <li>10<sup>3</sup> &divide; 2<sup>4</sup> = (10 &divide; 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 &times; y</sup>
- <ul>
- <li>(2<sup>2</sup>)<sup>3</sup> = 2<sup>2 &times; 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&nbsp;<sup><span class="frac"><sup>y</sup><span>&frasl;</span><sub>z</sub></span></sup> =
- <sup>z</sup><span><span class="sroot">x</span><sup style="font-size: small;">y</sup><span></span></span></p>
- <h2 id="fractional-exponent--examples">Examples</h2>
- <ul>
- <li>5&nbsp;<sup><span class="frac"><sup>1</sup><span>&frasl;</span><sub>2</sub></span></sup> =
- <sup>2</sup><span><span class="sroot">5</span></span></li>
- <li>7&nbsp;<sup><span class="frac"><sup>2</sup><span>&frasl;</span><sub>3</sub></span></sup> =
- <sup>3</sup><span><span class="sroot">7<sup>2</sup></span></span></li>
- </ul>
- <p><strong>Small Note:</strong> 2</sup><span class="sroot">x</span> or <span class="sroot">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="sroot">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>&UpperLeftArrow; 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>&frasl;</span><sub>4</sub></span> = <strong>-<span class="frac"><sup>3</sup><span>&frasl;</span><sub>4</sub></span></strong>
- </li>
- </ol>
- </section>
- </div>
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