Simplify cube root of -16a^3b^8

$\sqrt[3]{- 16 a^{3} b^{8}}$

Step 1

Rewrite $- 16 a^{3} b^{8}$ as ${(- 2 a b^{2})}^{3} \cdot (2 b^{2})$ .

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

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

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

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

Factor out $b^{6}$ .

$\sqrt[3]{{(- 2)}^{3} \cdot 2 a^{3} (b^{6} b^{2})}$

Rewrite $b^{6}$ as ${(b^{2})}^{3}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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