Simplify cube root of 128x^13y^6

$\sqrt[3]{128 x^{13} y^{6}}$

Step 1

Rewrite $128 x^{13} y^{6}$ as ${(4 x^{4} y^{2})}^{3} \cdot (2 x)$ .

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) x^{13} y^{6}}$

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} \cdot 2 x^{13} y^{6}}$

Factor out $x^{12}$ .

$\sqrt[3]{4^{3} \cdot 2 (x^{12} x) y^{6}}$

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

$\sqrt[3]{4^{3} \cdot 2 ({(x^{4})}^{3} x) y^{6}}$

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

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

Move $x$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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