Evaluate -9^(-3/2)

$- 9^{- \frac{3}{2}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{1}{9^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$- \frac{1}{{(3^{2})}^{\frac{3}{2}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{1}{3^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{1}{3^{2 (\frac{3}{2})}}$

Rewrite the expression.

$- \frac{1}{3^{3}}$

Raise $3$ to the power of $3$ .

$- \frac{1}{27}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{27}$

Decimal Form:

$- 0.\overline{037}$