<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-exponent-rules-ii" target="_blank">Exponent Rules II Exercise</a></p>
<p><strong>Note</strong>: around 1 minute into the video, we say that</p>
<p>(-2<sup>4</sup>)<sup>5</sup> = (-2)<sup>20</sup></p>
<p>The 4 should be inside its own bracket. In other words, we meant</p>
<p>((-2)<sup>4</sup>)<sup>5</sup> = (-2)<sup>20</sup></p>
<p>The reason this matters is otherwise some may think that (-2<sup>4</sup>) = -16.</p><p>There are numerous <strong><span style="color:#27ae60;">Exponent Rules</span></strong> we have to memorize.</p>
<ul>
<li><span style="color:#e74c3c;">Rule 6</span>: If you multiply two different numbers together with the same exponent, you can do the following:</li>
</ul>
<p>$$5^3 \times 3^3 = (5 \cdot 3)^3$$</p>
<p>$$(2 \cdot 9)^4 = 2^4 \cdot 9^4$$</p>
<ul>
<li><span style="color:#e74c3c;">Rule 7</span>: If you divide two different numbers with the same exponent, you can do the following:</li>
</ul>
<p>$$ \left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$$</p>
<p>$$ \left(\frac{7}{3}\right)^2 = \frac{7^2}{3^2}$$</p>
<ul>
<li><span style="color:#e74c3c;">Rule 8</span>: If you raise a number with an exponent to another exponent (with parentheses included), you simply multiply the exponents.</li>
</ul>
<p>$$(a^m)^n = a^{mn}$$</p>
<p>$$(2^5)^7 = 2^{35}$$</p>
<p><span style="font-size:20px;"><span style="color:#8e44ad;">Danger!!</span></span></p>
<p>$$5^{3^3} \neq 5^9$$</p>
<p>$$(5^3)^3 = 5^9$$</p>
<p>$$5^{3^3} = 5^{27}$$</p>