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

Apr 9, 2015

$\frac{1}{8}$

#### Explanation:

Firstly, you should change the 16 into the simplest base-power form.

$16 = {2}^{4}$

${16}^{- \frac{3}{4}} = {\left({2}^{4}\right)}^{- \frac{3}{4}}$

As we remember, the formula of multiplying powers, where
${\left({a}^{m}\right)}^{n} = {a}^{m n}$

Therefore,
${\left({2}^{4}\right)}^{- \frac{3}{4}} = {2}^{- \frac{12}{4}} = {2}^{-} 3$

Here we can apply the Indew law of ${a}^{-} n = \frac{1}{a} ^ n$
Hence, ${2}^{-} 3 = \frac{1}{2} ^ 3 = \frac{1}{8}$

${16}^{- \frac{3}{4}} = \frac{1}{8}$