# How do you simplify [(6x^-4z^3)/(2xz^-3)]^-1?

Sep 1, 2016

${x}^{5} / \left(3 {z}^{6}\right)$

#### Explanation:

There are a number of laws of indices involved here.
Do one step at a time.

${\left[\frac{6 {x}^{-} 4 {z}^{3}}{2 x {z}^{-} 3}\right]}^{\textcolor{red}{- 1}} \leftarrow$ Flip the fraction. Index changes sign.

${\left[\frac{\cancel{2} x \textcolor{b l u e}{{z}^{-} 3}}{{\cancel{6}}^{3} \textcolor{m a \ge n t a}{{x}^{-} 4} {z}^{3}}\right]}^{\textcolor{red}{+ 1}} \leftarrow \text{ cancel numbers, } {x}^{-} m = \frac{1}{x} ^ m$

$\frac{x \textcolor{m a \ge n t a}{{x}^{4}}}{3 {z}^{3} \textcolor{b l u e}{{z}^{3}}} \text{ } \leftarrow$ add indices of like bases.

${x}^{5} / \left(3 {z}^{6}\right)$