Simplify (3^2)^(-3/2)

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

Step 1

Multiply the exponents in ${(3^{2})}^{- \frac{3}{2}}$ .

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

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$3^{- 3}$

Step 2

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

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

Step 3

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

$\frac{1}{27}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{27}$

Decimal Form:

$0.\overline{037}$