Simplify fifth root of 64y^6

$\sqrt[5]{64 y^{6}}$

Step 1

Rewrite $64 y^{6}$ as ${(2 y)}^{5} \cdot (2 y)$ .

Factor $32$ out of $64$ .

$\sqrt[5]{32 (2) y^{6}}$

Rewrite $32$ as $2^{5}$ .

$\sqrt[5]{2^{5} \cdot 2 y^{6}}$

Factor out $y^{5}$ .

$\sqrt[5]{2^{5} \cdot 2 (y^{5} y)}$

Move $2$ .

$\sqrt[5]{2^{5} y^{5} \cdot 2 y}$

Rewrite $2^{5} y^{5}$ as ${(2 y)}^{5}$ .

$\sqrt[5]{{(2 y)}^{5} \cdot 2 y}$

Add parentheses.

$\sqrt[5]{{(2 y)}^{5} \cdot (2 y)}$

$\sqrt[5]{{(2 y)}^{5} \cdot (2 y)}$

Step 2

Pull terms out from under the radical.

$2 y \sqrt[5]{2 y}$

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