Simplify 2x^3 cube root of 125x^9y^7

$2 x^{3} \sqrt[3]{125 x^{9} y^{7}}$

Rewrite $125 x^{9} y^{7}$ as ${(5 x^{3} y^{2})}^{3} y$ .

Rewrite $125$ as $5^{3}$ .

$2 x^{3} \sqrt[3]{5^{3} x^{9} y^{7}}$

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

$2 x^{3} \sqrt[3]{5^{3} {(x^{3})}^{3} y^{7}}$

Factor out $y^{6}$ .

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

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

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

Rewrite $5^{3} {(x^{3})}^{3} {(y^{2})}^{3}$ as ${(5 x^{3} y^{2})}^{3}$ .

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

Pull terms out from under the radical.

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

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $3$ .

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

Multiply $5$ by $2$ .

$10 x^{6} y^{2} \sqrt[3]{y}$