Simplify the Radical Expression (3^(2/3))^(1/6)

${(3^{\frac{2}{3}})}^{\frac{1}{6}}$

Step 1

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

$3^{\frac{2}{3} \cdot \frac{1}{6}}$

Step 2

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Multiply $\frac{1}{3}$ by $\frac{1}{3}$ .

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

Step 4

Multiply $3$ by $3$ .

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