# How do you simplify (c^2/d)/(c^3/d^2)?

May 19, 2017

See a solution process below:

#### Explanation:

First, use this rule for dividing fractions to rewrite the expression:

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

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

Now, use these rule of exponents to simplify the $c$ terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$ and ${a}^{\textcolor{b l u e}{1}} = a$

$\frac{{c}^{\textcolor{red}{2}} {d}^{2}}{{c}^{\textcolor{b l u e}{3}} d} \implies {d}^{2} / \left({c}^{\textcolor{b l u e}{3} - \textcolor{red}{2}} d\right) \implies {d}^{2} / \left({c}^{1} d\right) \implies {d}^{2} / \left(c d\right)$

Now, use these rules of exponents to simplify the $d$ terms:

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

${d}^{2} / \left(c d\right) \implies {d}^{\textcolor{red}{2}} / \left(c {d}^{\textcolor{b l u e}{1}}\right) \implies {d}^{\textcolor{red}{2} - \textcolor{b l u e}{1}} / c \implies {d}^{1} / c \implies \frac{d}{c}$