Simplify cube root of -16a^12

$\sqrt[3]{- 16 a^{12}}$

Step 1

Rewrite $- 16 a^{12}$ as ${(- 2 a^{4})}^{3} \cdot 2$ .

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

$\sqrt[3]{- 8 (2) a^{12}}$

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

$\sqrt[3]{{(- 2)}^{3} \cdot 2 a^{12}}$

Rewrite $a^{12}$ as ${(a^{4})}^{3}$ .

$\sqrt[3]{{(- 2)}^{3} \cdot 2 {(a^{4})}^{3}}$

Move $2$ .

$\sqrt[3]{{(- 2)}^{3} {(a^{4})}^{3} \cdot 2}$

Rewrite ${(- 2)}^{3} {(a^{4})}^{3}$ as ${(- 2 a^{4})}^{3}$ .

$\sqrt[3]{{(- 2 a^{4})}^{3} \cdot 2}$

Step 2

Pull terms out from under the radical.

$- 2 a^{4} \sqrt[3]{2}$