Simplify fifth root of -64x^14y^20

$\sqrt[5]{- 64 x^{14} y^{20}}$

Step 1

Rewrite $- 64 x^{14} y^{20}$ as ${(- 2 x^{2} y^{4})}^{5} \cdot (2 x^{4})$ .

Factor $- 32$ out of $- 64$ .

$\sqrt[5]{- 32 (2) x^{14} y^{20}}$

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

$\sqrt[5]{{(- 2)}^{5} \cdot 2 x^{14} y^{20}}$

Factor out $x^{10}$ .

$\sqrt[5]{{(- 2)}^{5} \cdot 2 (x^{10} x^{4}) y^{20}}$

Rewrite $x^{10}$ as ${(x^{2})}^{5}$ .

$\sqrt[5]{{(- 2)}^{5} \cdot 2 ({(x^{2})}^{5} x^{4}) y^{20}}$

Rewrite $y^{20}$ as ${(y^{4})}^{5}$ .

$\sqrt[5]{{(- 2)}^{5} \cdot 2 ({(x^{2})}^{5} x^{4}) {(y^{4})}^{5}}$

Move $x^{4}$ .

$\sqrt[5]{{(- 2)}^{5} \cdot 2 ({(x^{2})}^{5}) {(y^{4})}^{5} x^{4}}$

Move $2$ .

$\sqrt[5]{({(- 2)}^{5} ({(x^{2})}^{5})) {(y^{4})}^{5} \cdot 2 x^{4}}$

Rewrite $({(- 2)}^{5} ({(x^{2})}^{5})) {(y^{4})}^{5}$ as ${(- 2 x^{2} y^{4})}^{5}$ .

$\sqrt[5]{{(- 2 x^{2} y^{4})}^{5} \cdot 2 x^{4}}$

Add parentheses.

$\sqrt[5]{{(- 2 x^{2} y^{4})}^{5} \cdot (2 x^{4})}$

Step 2

Pull terms out from under the radical.

$- 2 x^{2} y^{4} \sqrt[5]{2 x^{4}}$