# How do you simplify (16/81)^(-3/4)?

May 22, 2016

$\frac{27}{8}$

#### Explanation:

$16 = {2}^{4}$ and $81 = {3}^{4}$

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

A fraction raised to a negative index can be simplified by using its reciprocal raised to a positive index

${\left({3}^{4} / {2}^{4}\right)}^{\frac{3}{4}} = {\left(\frac{3}{2}\right)}^{3} = \frac{27}{8.}$