Simplify cube root of 128x^9y^17

$\sqrt[3]{128 x^{9} y^{17}}$

Step 1

Rewrite $128 x^{9} y^{17}$ as ${(4 x^{3} y^{5})}^{3} \cdot (2 y^{2})$ .

Factor $64$ out of $128$ .

$\sqrt[3]{64 (2) x^{9} y^{17}}$

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

$\sqrt[3]{4^{3} \cdot 2 x^{9} y^{17}}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$\sqrt[3]{4^{3} \cdot 2 {(x^{3})}^{3} y^{17}}$

Factor out $y^{15}$ .

$\sqrt[3]{4^{3} \cdot 2 {(x^{3})}^{3} (y^{15} y^{2})}$

Rewrite $y^{15}$ as ${(y^{5})}^{3}$ .

$\sqrt[3]{4^{3} \cdot 2 {(x^{3})}^{3} ({(y^{5})}^{3} y^{2})}$

Move $2$ .

$\sqrt[3]{4^{3} {(x^{3})}^{3} {(y^{5})}^{3} \cdot 2 y^{2}}$

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

$\sqrt[3]{{(4 x^{3} y^{5})}^{3} \cdot 2 y^{2}}$

Add parentheses.

$\sqrt[3]{{(4 x^{3} y^{5})}^{3} \cdot (2 y^{2})}$

Step 2

Pull terms out from under the radical.

$4 x^{3} y^{5} \sqrt[3]{2 y^{2}}$