Simplify ( cube root of 2)^9

${(\sqrt[3]{2})}^{9}$

Step 1

Rewrite ${\sqrt[3]{2}}^{9}$ as $2^{3}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

${(2^{\frac{1}{3}})}^{9}$

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

$2^{\frac{1}{3} \cdot 9}$

Combine $\frac{1}{3}$ and $9$ .

$2^{\frac{9}{3}}$

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3$ by $1$ .

$2^{3}$

Step 2

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

$8$