Simplify the Radical Expression cube root of -8xy^12

$\sqrt[3]{- 8 x y^{12}}$

Step 1

Rewrite $- 8 x y^{12}$ as ${(- 2 y^{4})}^{3} x$ .

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$\sqrt[3]{{(- 2)}^{3} x y^{12}}$

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

$\sqrt[3]{{(- 2)}^{3} x {(y^{4})}^{3}}$

Move $x$ .

$\sqrt[3]{{(- 2)}^{3} {(y^{4})}^{3} x}$

Rewrite ${(- 2)}^{3} {(y^{4})}^{3}$ as ${(- 2 y^{4})}^{3}$ .

$\sqrt[3]{{(- 2 y^{4})}^{3} x}$

Step 2

Pull terms out from under the radical.

$- 2 y^{4} \sqrt[3]{x}$