<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-exponent-rules-i">Exponent Rules I Exercise</a></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 1</span>: If $a^n = a^m$, then $n=m$. Tthis works if $a$ doesn't equal $0$ or $1$.</li>
</ul>
<p>$$5^x = 5^{y+2}$$</p>
<p>$$x = y+2$$</p>
<ul>
<li><span style="color:#e74c3c;">Rule 2</span>: If you have a negative exponent, you can make it positive by "flipping" the fraction.</li>
</ul>
<p>$$5^{-3} = \frac{1}{5^3}$$</p>
<p>$$\frac{2}{3^{-3}} \rightarrow 2 \times \frac{1}{3^{-3}} \rightarrow 2 \times 3^3$$</p>
<ul>
<li><span style="color:#e74c3c;">Rule 3</span>: If you multiply two numbers together with the same base, you can add the exponents.</li>
</ul>
<p>$$a^n \times a^m = a^{n+m}$$</p>
<p>$$3^5 \times 3^7 = 3^{12}$$</p>
<ul>
<li><span style="color:#e74c3c;">Rule 4</span>: If you divide a number by another number with the same base, you can subtract the exponents.</li>
</ul>
<p>$$\frac{a^n}{a^m} = a^{n-m}$$</p>
<p>$$\frac{7^7}{7^3} = 7^4$$</p>
<ul>
<li><span style="color:#e74c3c;">Rule 5</span>: If you raise anything to the $0$ power, it equals $1$, except in the $0^0$ case, which is undefined.</li>
</ul>
<p>$$874^0 = 1$$</p>