# How do you simplify and write c^-3/d^-5 with positive exponents?

##### 2 Answers
Feb 20, 2017

See the entire simplification process below:

#### Explanation:

We will use these two rules of exponents to eliminate the negative exponents:

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

${c}^{\textcolor{red}{- 3}} / {d}^{\textcolor{b l u e}{- 5}} = {d}^{\textcolor{b l u e}{- - 5}} / {c}^{\textcolor{red}{- - 3}} = {d}^{\textcolor{b l u e}{5}} / {c}^{\textcolor{red}{3}}$

Feb 20, 2017

${d}^{5} / {c}^{3}$

#### Explanation:

${c}^{-} \frac{3}{d} ^ - 5$

$\therefore = {c}^{-} 3 \div {d}^{-} 5$

$\therefore = \frac{1}{c} ^ 3 \div \frac{1}{d} ^ - 5$

$\therefore = \frac{1}{c} ^ 3 \div \frac{\frac{1}{1}}{{d}^{5}}$

$\therefore = \frac{1}{c} ^ 3 \times \left(\frac{1}{1} \times {d}^{5} / 1\right)$

$\therefore = \frac{1}{c} ^ 3 \times {d}^{5} / 1$

$\therefore = {d}^{5} / {c}^{3}$