Question

Find the quotient. rac{5^6}{5^5} " alt=" \frac{5^6}{5^5} " align="absmiddle" class="latex-formula">

Answer 1

To the risk of sounding redundant.

$\bf a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------\\\\ \cfrac{5^6}{5^5}\implies 5^6\cdot 5^{-5}\implies 5^{6-5}\implies 5^1\implies 5$

Answer 2

We can solve this problem by using the laws of exponents. The laws of exponents state:

$\frac{x^{n} }{x^{y} }$ = $x^{n-y}$

We can use this law in our situation. The answer here, using the laws of exponents, is $5^{6-5}$ or 5.