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

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

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

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

$\sqrt[3]{{(- 2)}^{3} a^{8} b^{5}}$

Factor out $a^{6}$ .

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

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

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

Factor out $b^{3}$ .

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

Move $a^{2}$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

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