Evaluate (1/81)^(-3/4)

${(\frac{1}{81})}^{- \frac{3}{4}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 2

Simplify the expression.

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

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

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

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

Step 3

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{3}$

Step 4

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

$27$