# How do you simplify (-64)^(-2/3)?

Mar 7, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

${\left(- 64\right)}^{- 2 \times \frac{1}{3}}$

Next, use this rule of exponents to separate the exponents:

${x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}} = {\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}}$

${\left(- 64\right)}^{\textcolor{red}{- 2} \times \textcolor{b l u e}{\frac{1}{3}}} \implies {\left(- {64}^{\textcolor{red}{- 2}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}}$

Then, use this rule of exponents to eliminate the negative exponent:

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

${\left(- {64}^{\textcolor{red}{- 2}}\right)}^{\frac{1}{3}} \implies {\left(\frac{1}{-} {64}^{\textcolor{red}{- - 2}}\right)}^{\frac{1}{3}} \implies {\left(\frac{1}{-} {64}^{\textcolor{red}{2}}\right)}^{\frac{1}{3}} \implies$

${\left(\frac{1}{4096}\right)}^{\frac{1}{3}} \implies \frac{1}{16}$