Simplify the Radical Expression ( cube root of -16)^3

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

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

Factor $- 8$ out of $- 16$ .

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

Rewrite $- 8$ as ${(- 2)}^{3}$ .

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

Pull terms out from under the radical.

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

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

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

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

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

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.

$- 8 \cdot 2$

Multiply $- 8$ by $2$ .

$- 16$