How do you simplify 9 ^ (-3/2)?

Oct 7, 2015

$\frac{1}{27}$

Explanation:

${9}^{- \frac{3}{2}}$
$\textcolor{w h i t e}{\text{XXX}} = \frac{1}{{9}^{\frac{3}{2}}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{1}{{\left({9}^{\frac{1}{2}}\right)}^{3}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{1}{{3}^{3}}$ (see note below)

$\textcolor{w h i t e}{\text{XXX}} = \frac{1}{27}$

Noite: In taking the square root of $9$ I only extracted the primary root;
a secondary solution exists $\frac{1}{{\left(- 3\right)}^{3}} = - \frac{1}{27}$