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How do you simplify $9^{- \frac{3}{2}}$ $9 ^ (-3/2)$ ?

1 Answer

Oct 7, 2015

$\frac{1}{27}$ $1/27$

Explanation:

$9^{- \frac{3}{2}}$ $9^(-3/2)$
$XXX = \frac{1}{9^{\frac{3}{2}}}$ $color(white)("XXX")=1/(9^(3/2))$

$XXX = \frac{1}{{(9^{\frac{1}{2}})}^{3}}$ $color(white)("XXX")=1/((9^(1/2))^3)$

$XXX = \frac{1}{3^{3}}$ $color(white)("XXX")=1/(3^3)$ (see note below)

$XXX = \frac{1}{27}$ $color(white)("XXX")=1/27$

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

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