Simplify ( cube root of 16)^3

${(\sqrt[3]{16})}^{3}$

Step 1

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

${\sqrt[3]{8 (2)}}^{3}$

Rewrite $8$ as $2^{3}$ .

${\sqrt[3]{2^{3} \cdot 2}}^{3}$

Step 2

Pull terms out from under the radical.

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

Step 3

Simplify the expression.

Apply the product rule to $2 \sqrt[3]{2}$ .

$2^{3} {\sqrt[3]{2}}^{3}$

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

$8 {\sqrt[3]{2}}^{3}$

Step 4

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

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

$8 {(2^{\frac{1}{3}})}^{3}$

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

$8 \cdot 2^{\frac{1}{3} \cdot 3}$

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

$8 \cdot 2^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 \cdot 2^{\frac{3}{3}}$

Rewrite the expression.

$8 \cdot 2^{1}$

Evaluate the exponent.

$8 \cdot 2$

Step 5

Multiply $8$ by $2$ .

$16$