Simplify sixth root of 64a^6b^7

$\sqrt[6]{64 a^{6} b^{7}}$

Step 1

Rewrite $64 a^{6} b^{7}$ as ${(2 a b)}^{6} b$ .

Rewrite $64$ as $2^{6}$ .

$\sqrt[6]{2^{6} a^{6} b^{7}}$

Factor out $b^{6}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

$2 a b \sqrt[6]{b}$

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