Evaluate 81^(-3/4)

$81^{- \frac{3}{4}}$

Step 1

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

$\frac{1}{81^{\frac{3}{4}}}$

Step 2

Simplify the denominator.

Rewrite $81$ as $3^{4}$ .

$\frac{1}{{(3^{4})}^{\frac{3}{4}}}$

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

$\frac{1}{3^{4 (\frac{3}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{1}{3^{4 (\frac{3}{4})}}$

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:

$0.\overline{037}$