Simplify ( cube root of 3)^6

${(\sqrt[3]{3})}^{6}$

Step 1

Rewrite ${\sqrt[3]{3}}^{6}$ as $3^{2}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{3}$ as $3^{\frac{1}{3}}$ .

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

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

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

Combine $\frac{1}{3}$ and $6$ .

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

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 $1$ .

$3^{2}$

Step 2

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

$9$