Simplify the Radical Expression - cube root of -48x^5y^6

$- \sqrt[3]{- 48 x^{5} y^{6}}$

Step 1

Rewrite $- 48 x^{5} y^{6}$ as ${(- 2 x y^{2})}^{3} \cdot (6 x^{2})$ .

Factor $- 8$ out of $- 48$ .

$- \sqrt[3]{- 8 (6) x^{5} y^{6}}$

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

$- \sqrt[3]{{(- 2)}^{3} \cdot 6 x^{5} y^{6}}$

Factor out $x^{3}$ .

$- \sqrt[3]{{(- 2)}^{3} \cdot 6 (x^{3} x^{2}) y^{6}}$

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

$- \sqrt[3]{{(- 2)}^{3} \cdot 6 (x^{3} x^{2}) {(y^{2})}^{3}}$

Move $x^{2}$ .

$- \sqrt[3]{{(- 2)}^{3} \cdot 6 (x^{3}) {(y^{2})}^{3} x^{2}}$

Move $6$ .

$- \sqrt[3]{{(- 2)}^{3} (x^{3}) {(y^{2})}^{3} \cdot 6 x^{2}}$

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

$- \sqrt[3]{{(- 2 x y^{2})}^{3} \cdot 6 x^{2}}$

Add parentheses.

$- \sqrt[3]{{(- 2 x y^{2})}^{3} \cdot (6 x^{2})}$

Step 2

Pull terms out from under the radical.

$- (- 2 x y^{2} \sqrt[3]{6 x^{2}})$

Step 3

Multiply $- 2$ by $- 1$ .

$2 x y^{2} \sqrt[3]{6 x^{2}}$