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

Sep 12, 2016

$\frac{1}{27 {x}^{6}}$

#### Explanation:

Recall: two of the laws of indices:

${x}^{\textcolor{red}{- m}} = \frac{1}{x} ^ \textcolor{red}{m} \text{ and } {\left(a b\right)}^{m} = {a}^{m} {b}^{m}$

Let's get rid of the negative index first....

${\left(3 {x}^{2}\right)}^{\textcolor{red}{- 3}} = \frac{1}{3 {x}^{2}} ^ \textcolor{red}{3} \text{ } \leftarrow$ remove brackets.

=$\frac{1}{{3}^{3} {x}^{6}}$

=$\frac{1}{27 {x}^{6}}$