Simplify fifth root of -32x^15y^2

$\sqrt[5]{- 32 x^{15} y^{2}}$

Step 1

Rewrite $- 32 x^{15} y^{2}$ as ${(- 2 x^{3})}^{5} y^{2}$ .

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

$\sqrt[5]{{(- 2)}^{5} x^{15} y^{2}}$

Rewrite $x^{15}$ as ${(x^{3})}^{5}$ .

$\sqrt[5]{{(- 2)}^{5} {(x^{3})}^{5} y^{2}}$

Rewrite ${(- 2)}^{5} {(x^{3})}^{5}$ as ${(- 2 x^{3})}^{5}$ .

$\sqrt[5]{{(- 2 x^{3})}^{5} y^{2}}$

Step 2

Pull terms out from under the radical.

$- 2 x^{3} \sqrt[5]{y^{2}}$