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

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

Simplify the expression.

Move $81^{- \frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{3}$

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

$27$