Algebra Examples

$\frac{\sqrt[3]{32 x^{5} y^{7}}}{\sqrt[3]{4 x^{2} y^{4}}}$

Step 1

Combine $\sqrt[3]{32 x^{5} y^{7}}$ and $\sqrt[3]{4 x^{2} y^{4}}$ into a single radical.

$\sqrt[3]{\frac{32 x^{5} y^{7}}{4 x^{2} y^{4}}}$

Step 2

Reduce the expression $\frac{32 x^{5} y^{7}}{4 x^{2} y^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $4$ out of $32 x^{5} y^{7}$ .

$\sqrt[3]{\frac{4 (8 x^{5} y^{7})}{4 x^{2} y^{4}}}$

Step 2.2

Factor $4$ out of $4 x^{2} y^{4}$ .

$\sqrt[3]{\frac{4 (8 x^{5} y^{7})}{4 (x^{2} y^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{4 (8 x^{5} y^{7})}{4 (x^{2} y^{4})}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{5} y^{7}}{x^{2} y^{4}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $8 x^{5} y^{7}$ .

$\sqrt[3]{\frac{x^{2} (8 x^{3} y^{7})}{x^{2} y^{4}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{2}$ out of $x^{2} y^{4}$ .

$\sqrt[3]{\frac{x^{2} (8 x^{3} y^{7})}{x^{2} (y^{4})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (8 x^{3} y^{7})}{x^{2} y^{4}}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{3} y^{7}}{y^{4}}}$

Step 4

Cancel the common factor of $y^{7}$ and $y^{4}$ .

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Step 4.1

Factor $y^{4}$ out of $8 x^{3} y^{7}$ .

$\sqrt[3]{\frac{y^{4} (8 x^{3} y^{3})}{y^{4}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\sqrt[3]{\frac{y^{4} (8 x^{3} y^{3})}{y^{4} \cdot 1}}$

Step 4.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y^{4} (8 x^{3} y^{3})}{y^{4} \cdot 1}}$

Step 4.2.3

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{3} y^{3}}{1}}$

Step 4.2.4

Divide $8 x^{3} y^{3}$ by $1$ .

$\sqrt[3]{8 x^{3} y^{3}}$

Step 5

Rewrite $8 x^{3} y^{3}$ as ${(2 x y)}^{3}$ .

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

Step 6

Pull terms out from under the radical, assuming real numbers.

$2 x y$