Simplify cube root of -64a^8b^5

$\sqrt[3]{- 64 a^{8} b^{5}}$

Step 1

Rewrite $- 64 a^{8} b^{5}$ as ${(- 4 a^{2} b)}^{3} (a^{2} b^{2})$ .

Rewrite $- 64$ as ${(- 4)}^{3}$ .

$\sqrt[3]{{(- 4)}^{3} a^{8} b^{5}}$

Factor out $a^{6}$ .

$\sqrt[3]{{(- 4)}^{3} (a^{6} a^{2}) b^{5}}$

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

$\sqrt[3]{{(- 4)}^{3} ({(a^{2})}^{3} a^{2}) b^{5}}$

Factor out $b^{3}$ .

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

Move $a^{2}$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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