Simplify the Radical Expression ( cube root of 250x^7y^3)/( cube root of 2x^2y)

$\frac{\sqrt[3]{250 x^{7} y^{3}}}{\sqrt[3]{2 x^{2} y}}$

Step 1

Combine $\sqrt[3]{250 x^{7} y^{3}}$ and $\sqrt[3]{2 x^{2} y}$ into a single radical.

$\sqrt[3]{\frac{250 x^{7} y^{3}}{2 x^{2} y}}$

Step 2

Reduce the expression $\frac{250 x^{7} y^{3}}{2 x^{2} y}$ by cancelling the common factors.

Factor $2$ out of $250 x^{7} y^{3}$ .

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

Factor $2$ out of $2 x^{2} y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{7}$ and $x^{2}$ .

Factor $x^{2}$ out of $125 x^{7} y^{3}$ .

$\sqrt[3]{\frac{x^{2} (125 x^{5} y^{3})}{x^{2} y}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} y$ .

$\sqrt[3]{\frac{x^{2} (125 x^{5} y^{3})}{x^{2} (y)}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (125 x^{5} y^{3})}{x^{2} y}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{5} y^{3}}{y}}$

Step 4

Cancel the common factor of $y^{3}$ and $y$ .

Factor $y$ out of $125 x^{5} y^{3}$ .

$\sqrt[3]{\frac{y (125 x^{5} y^{2})}{y}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{y (125 x^{5} y^{2})}{y^{1}}}$

Factor $y$ out of $y^{1}$ .

$\sqrt[3]{\frac{y (125 x^{5} y^{2})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{y (125 x^{5} y^{2})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{5} y^{2}}{1}}$

Divide $125 x^{5} y^{2}$ by $1$ .

$\sqrt[3]{125 x^{5} y^{2}}$

Step 5

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

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

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

Factor out $x^{3}$ .

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

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

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

Add parentheses.

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

Step 6

Pull terms out from under the radical.

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

Simplify the Radical Expression ( cube root of 250x^7y^3)/( cube root of 2x^2y)

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