Algebra Examples

$\frac{\sqrt[3]{625 x^{6} y^{4}}}{\sqrt[3]{5 x y}}$

Step 1

Combine $\sqrt[3]{625 x^{6} y^{4}}$ and $\sqrt[3]{5 x y}$ into a single radical.

$\sqrt[3]{\frac{625 x^{6} y^{4}}{5 x y}}$

Step 2

Reduce the expression $\frac{625 x^{6} y^{4}}{5 x y}$ by cancelling the common factors.

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Step 2.1

Factor $5$ out of $625 x^{6} y^{4}$ .

$\sqrt[3]{\frac{5 (125 x^{6} y^{4})}{5 x y}}$

Step 2.2

Factor $5$ out of $5 x y$ .

$\sqrt[3]{\frac{5 (125 x^{6} y^{4})}{5 (x y)}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{5 (125 x^{6} y^{4})}{5 (x y)}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{6} y^{4}}{x y}}$

Step 3

Cancel the common factor of $x^{6}$ and $x$ .

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Step 3.1

Factor $x$ out of $125 x^{6} y^{4}$ .

$\sqrt[3]{\frac{x (125 x^{5} y^{4})}{x y}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $x y$ .

$\sqrt[3]{\frac{x (125 x^{5} y^{4})}{x (y)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{x (125 x^{5} y^{4})}{x y}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{5} y^{4}}{y}}$

Step 4

Cancel the common factor of $y^{4}$ and $y$ .

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Step 4.1

Factor $y$ out of $125 x^{5} y^{4}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

Divide $125 x^{5} y^{3}$ by $1$ .

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Factor out $x^{3}$ .

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

Step 5.3

Move $x^{2}$ .

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

Step 5.4

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

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

Step 6

Pull terms out from under the radical.

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