Simplify (-27)^(2/3)(81^(1/4))

${(- 27)}^{\frac{2}{3}} (81^{\frac{1}{4}})$

Simplify the expression.

Rewrite $- 27$ as ${(- 3)}^{3}$ .

${({(- 3)}^{3})}^{\frac{2}{3}} \cdot 81^{\frac{1}{4}}$

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

${(- 3)}^{3 (\frac{2}{3})} \cdot 81^{\frac{1}{4}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(- 3)}^{3 (\frac{2}{3})} \cdot 81^{\frac{1}{4}}$

Rewrite the expression.

${(- 3)}^{2} \cdot 81^{\frac{1}{4}}$

Simplify the expression.

Raise $- 3$ to the power of $2$ .

$9 \cdot 81^{\frac{1}{4}}$

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

$9 \cdot {(3^{4})}^{\frac{1}{4}}$

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

$9 \cdot 3^{4 (\frac{1}{4})}$

Cancel the common factor of $4$ .

Cancel the common factor.

$9 \cdot 3^{4 (\frac{1}{4})}$

Rewrite the expression.

$9 \cdot 3^{1}$

Evaluate the exponent.

$9 \cdot 3$

Multiply $9$ by $3$ .

$27$