# How do you simplify (x^2y^-1)^2 and write it using only positive exponents?

Oct 2, 2016

$= {x}^{4} / {y}^{2}$

#### Explanation:

Recall these laws of indices:

${\left(x y\right)}^{m} = {x}^{m} {y}^{m} \text{ and "(x^m)^n = x^(mn)" and } {x}^{-} m = \frac{1}{x} ^ m$

The laws can be be used in any order.

${\left({x}^{2} \textcolor{red}{{y}^{-} 1}\right)}^{2} \text{ " rarr" } {\left({x}^{2} / \textcolor{red}{y}\right)}^{2} \textcolor{w h i t e}{\times \times \times \times x} \left(\textcolor{red}{{x}^{-} m = \frac{1}{x} ^ m}\right)$

$= {x}^{4} / {y}^{2}$