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

Apr 17, 2016

$= \frac{1}{9 {x}^{6}}$

#### Explanation:

Use the power rule :
${\left({x}^{a}\right)}^{b} = {x}^{a \times b}$
-

So in this case we have
${\left(- 3 {x}^{3}\right)}^{- 2}$
Thus, we need to distribute the -2 exponent to the terms in the parenthesis:
$- {3}^{- 2} \times {x}^{3 \times - 2}$

Since -3 is raised to a negative power, we need to do:
$\frac{1}{- {3}^{2}}$
The same thing needs to be done with ${x}^{- 6}$ to make it into a positive exponent:
$\frac{1}{x} ^ 6$

We now have
$\frac{1}{- {3}^{2}} \times \frac{1}{x} ^ \left\{6\right\}$

Note that since -3 is raised to a power that is of even number, the product will eventually be positive ($- 3 \times - 3 = 9$). So we can take out the negative sign to get:

$\frac{1}{{3}^{2}} \times \frac{1}{x} ^ \left\{6\right\}$
$= \frac{1}{9 {x}^{6}}$