# How do you simplify (a^2/b^3)/(b^5/a)?

Apr 30, 2017

See the solution process below:

#### Explanation:

First, use this rule for dividing fractions:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{{a}^{2}}}{\textcolor{b l u e}{{b}^{3}}}}{\frac{\textcolor{g r e e n}{{b}^{5}}}{\textcolor{p u r p \le}{a}}} = \frac{\textcolor{red}{{a}^{2}} \times \textcolor{p u r p \le}{a}}{\textcolor{b l u e}{{b}^{3}} \times \textcolor{g r e e n}{{b}^{5}}}$

Now, use these two rules of exponents to multiply the terms in the numerator and denominator:

$a = {a}^{\textcolor{red}{1}}$ and ${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\frac{\textcolor{red}{{a}^{2}} \times \textcolor{p u r p \le}{a}}{\textcolor{b l u e}{{b}^{3}} \times \textcolor{g r e e n}{{b}^{5}}} = \frac{\textcolor{red}{{a}^{2}} \times \textcolor{p u r p \le}{{a}^{1}}}{\textcolor{b l u e}{{b}^{3}} \times \textcolor{g r e e n}{{b}^{5}}} = {a}^{\textcolor{red}{2} + \textcolor{p u r p \le}{1}} / {b}^{\textcolor{b l u e}{3} + \textcolor{g r e e n}{5}} = {a}^{3} / {b}^{8}$