Evaluate 81^(-3/2)

$81^{- \frac{3}{2}}$

Step 1

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

$\frac{1}{81^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

Rewrite $81$ as $9^{2}$ .

$\frac{1}{{(9^{2})}^{\frac{3}{2}}}$

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

$\frac{1}{9^{2 (\frac{3}{2})}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{9^{2 (\frac{3}{2})}}$

Rewrite the expression.

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

Raise $9$ to the power of $3$ .

$\frac{1}{729}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{729}$

Decimal Form:

$0.00137174 \dots$