# How do you simplify (8^(-1/2))^(-2/3)?

Jun 16, 2016

${\left({8}^{- \frac{1}{2}}\right)}^{- \frac{2}{3}} = 2$

#### Explanation:

As ${\left({a}^{m}\right)}^{n} = {a}^{m \times n}$

${\left({8}^{- \frac{1}{2}}\right)}^{- \frac{2}{3}}$

= ${8}^{\left(- \frac{1}{2}\right) \times \left(- \frac{2}{3}\right)}$

= ${8}^{\frac{1}{3}}$

but $8 = {2}^{3}$, hence above is equal to

= ${\left({2}^{3}\right)}^{\frac{1}{3}}$

= ${2}^{3 \times \frac{1}{3}}$

= ${2}^{1} = 2$