# How do you simplify (x^-2)^3?

Feb 13, 2017

See the entire simplification process below:

#### Explanation:

Use this rule of exponents to simplify: ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({x}^{\textcolor{red}{- 2}}\right)}^{\textcolor{b l u e}{3}} = {x}^{\textcolor{red}{- 2} \times \textcolor{b l u e}{3}} = {x}^{-} 6$

If as part of the simplification process you want to have only positive exponents you can use this rule for exponents: ${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${x}^{\textcolor{red}{- 6}} = \frac{1}{x} ^ \textcolor{red}{- - 6} = \frac{1}{x} ^ 6$

The simplification is ${x}^{-} 6$ or $\frac{1}{x} ^ 6$