Simplify the Radical Expression 3^(1/3)*9^(1/3)

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

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

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

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

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

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

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

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

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

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

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

Combine the numerators over the common denominator.

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

Add $1$ and $2$ .

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$3^{1}$

Evaluate the exponent.

$3$