Simplify the Radical Expression cube root of -125xy^12

$\sqrt[3]{- 125 x y^{12}}$

Rewrite $- 125 x y^{12}$ as ${(- 5 y^{4})}^{3} x$ .

Rewrite $- 125$ as ${(- 5)}^{3}$ .

$\sqrt[3]{{(- 5)}^{3} x y^{12}}$

Rewrite $y^{12}$ as ${(y^{4})}^{3}$ .

$\sqrt[3]{{(- 5)}^{3} x {(y^{4})}^{3}}$

Move $x$ .

$\sqrt[3]{{(- 5)}^{3} {(y^{4})}^{3} x}$

Rewrite ${(- 5)}^{3} {(y^{4})}^{3}$ as ${(- 5 y^{4})}^{3}$ .

$\sqrt[3]{{(- 5 y^{4})}^{3} x}$

Pull terms out from under the radical.

$- 5 y^{4} \sqrt[3]{x}$