# How do you simplify (5^2/8^2)^(-1/2)?

Feb 20, 2017

See the entire simplification process below:

#### Explanation:

Use this rule of exponents to simplify this expression:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({5}^{\textcolor{red}{2}} / {8}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{- \frac{1}{2}}} = {5}^{\textcolor{red}{2} \times \textcolor{b l u e}{- \frac{1}{2}}} / {8}^{\textcolor{red}{2} \times \textcolor{b l u e}{- \frac{1}{2}}} = {5}^{-} \frac{1}{8} ^ - 1$

Next, use these rules for exponents to eliminate the negative exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$ and $\frac{1}{x} ^ \textcolor{red}{a} = {x}^{\textcolor{red}{- a}}$

${5}^{\textcolor{red}{- 1}} / {8}^{\textcolor{red}{- 1}} = {8}^{\textcolor{red}{- - 1}} / {5}^{\textcolor{red}{- - 1}} = {8}^{1} / {5}^{1}$

Now, use this rule of exponents to complete the simplification:

${a}^{\textcolor{red}{1}} = a$

${8}^{\textcolor{red}{1}} / {5}^{\textcolor{red}{1}} = \frac{8}{5}$