Simplify fifth root of -32x^6y

$\sqrt[5]{- 32 x^{6} y}$

Step 1

Rewrite $- 32 x^{6} y$ as ${(- 2 x)}^{5} (x y)$ .

Rewrite $- 32$ as ${(- 2)}^{5}$ .

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

Factor out $x^{5}$ .

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

Rewrite ${(- 2)}^{5} x^{5}$ as ${(- 2 x)}^{5}$ .

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

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

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