Simplify 9^(1/3)*81^(1/3)

$9^{\frac{1}{3}} \cdot 81^{\frac{1}{3}}$

Multiply $9^{\frac{1}{3}} \cdot 81^{\frac{1}{3}}$ .

Rewrite $9$ as $3^{2}$ .

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

Multiply the exponents in ${(3^{2})}^{\frac{1}{3}}$ .

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

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

Combine $2$ and $\frac{1}{3}$ .

$3^{\frac{2}{3}} \cdot 81^{\frac{1}{3}}$

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

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

Multiply the exponents in ${(3^{4})}^{\frac{1}{3}}$ .

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

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

Combine $4$ and $\frac{1}{3}$ .

$3^{\frac{2}{3}} \cdot 3^{\frac{4}{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3^{\frac{2}{3} + \frac{4}{3}}$

Combine the numerators over the common denominator.

$3^{\frac{2 + 4}{3}}$

Add $2$ and $4$ .

$3^{\frac{6}{3}}$

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

$3^{\frac{3 \cdot 2}{3 \cdot 1}}$

Rewrite the expression.

$3^{\frac{2}{1}}$

Divide $2$ by $1$ .

$3^{2}$

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

$9$