# How do you simplify (x^-2y^2)^-3 and write it using only positive exponents?

Mar 27, 2017

See the entire solution process below:

#### Explanation:

First, use this rule for exponents to eliminate the outer exponent:

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

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

Now, use this rule for exponents to eliminate the negative exponent:

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

${x}^{6} {y}^{\textcolor{red}{- 6}} = {x}^{6} / {y}^{\textcolor{red}{- - 6}} = {x}^{6} / {y}^{\textcolor{red}{6}}$