# How do you simplify [(-3 times 3^(1/2))^(-1/3)]?

Jun 30, 2016

$- \frac{i}{3}$

#### Explanation:

${\left({x}^{a}\right)}^{b} = {x}^{a \cdot b}$

and

$\left({x}^{a}\right) \cdot \left({x}^{b}\right) = {x}^{a + b}$

and

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

So:

• $\left(- {3}^{- \frac{1}{3}} \cdot {3}^{- \frac{1}{6}}\right)$

• $- {9}^{- \frac{1}{2}}$

• $\frac{1}{- {9}^{\frac{1}{2}}}$

• $\frac{1}{\sqrt{- 9}}$

• $\frac{1}{3 i}$

• $- \frac{i}{3}$