Simplify 2y^3 cube root of 375x^7y^3

$2 y^{3} \sqrt[3]{375 x^{7} y^{3}}$

Rewrite $375 x^{7} y^{3}$ as ${(5 x^{2} y)}^{3} \cdot (3 x)$ .

Factor $125$ out of $375$ .

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

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

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

Factor out $x^{6}$ .

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

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

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

Move $x$ .

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

Move $3$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

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

Move $y$ .

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

Multiply $y$ by $y^{3}$ .

Raise $y$ to the power of $1$ .

$2 (y^{1} y^{3}) (5 x^{2} \sqrt[3]{3 x})$

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

$2 y^{1 + 3} (5 x^{2} \sqrt[3]{3 x})$

Add $1$ and $3$ .

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

Multiply $5$ by $2$ .

$10 y^{4} x^{2} \sqrt[3]{3 x}$