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

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

Simplify the expression.

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$3 {(27)}^{\frac{2}{3}}$

Simplify the expression.

Rewrite $27$ as $3^{3}$ .

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

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

$3 \cdot 3^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \cdot 3^{3 (\frac{2}{3})}$

Rewrite the expression.

$3 \cdot 3^{2}$

Simplify the expression.

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

$3 \cdot 9$

Multiply $3$ by $9$ .

$27$