# How do you simplify 4(8)^(-2/3)?

Apr 16, 2017

The negative index means that the base can be moved to the denominator and become positive.

$4 {\left(8\right)}^{- \frac{2}{3}}$

$= \frac{4}{8} ^ \left(\frac{2}{3}\right)$

A fractional index can be written as an index and a root.

$= \frac{4}{{\sqrt[3]{8}}^{2}}$

$= \frac{4}{2} ^ 2$

$= \frac{4}{4}$

$= 1$