Algebra Examples

$\sqrt[3]{\frac{432 x^{8} y^{4}}{125 x^{2} y^{7}}}$

Step 1

Reduce the expression $\frac{432 x^{8} y^{4}}{125 x^{2} y^{7}}$ by cancelling the common factors.

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Step 1.1

Factor $x^{2}$ out of $432 x^{8} y^{4}$ .

$\sqrt[3]{\frac{x^{2} (432 x^{6} y^{4})}{125 x^{2} y^{7}}}$

Step 1.2

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

$\sqrt[3]{\frac{x^{2} (432 x^{6} y^{4})}{x^{2} (125 y^{7})}}$

Step 1.3

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (432 x^{6} y^{4})}{x^{2} (125 y^{7})}}$

Step 1.4

Rewrite the expression.

$\sqrt[3]{\frac{432 x^{6} y^{4}}{125 y^{7}}}$

Step 2

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

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Step 2.1

Factor $y^{4}$ out of $432 x^{6} y^{4}$ .

$\sqrt[3]{\frac{y^{4} (432 x^{6})}{125 y^{7}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $y^{4}$ out of $125 y^{7}$ .

$\sqrt[3]{\frac{y^{4} (432 x^{6})}{y^{4} (125 y^{3})}}$

Step 2.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y^{4} (432 x^{6})}{y^{4} (125 y^{3})}}$

Step 2.2.3

Rewrite the expression.

$\sqrt[3]{\frac{432 x^{6}}{125 y^{3}}}$

Step 3

Rewrite $\frac{432 x^{6}}{125 y^{3}}$ as ${(\frac{6 x^{2}}{5 y})}^{3} \cdot 2$ .

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Step 3.1

Factor the perfect power ${(6 x^{2})}^{3}$ out of $432 x^{6}$ .

$\sqrt[3]{\frac{{(6 x^{2})}^{3} \cdot 2}{125 y^{3}}}$

Step 3.2

Factor the perfect power ${(5 y)}^{3}$ out of $125 y^{3}$ .

$\sqrt[3]{\frac{{(6 x^{2})}^{3} \cdot 2}{{(5 y)}^{3} \cdot 1}}$

Step 3.3

Rearrange the fraction $\frac{{(6 x^{2})}^{3} \cdot 2}{{(5 y)}^{3} \cdot 1}$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

Combine $\frac{6 x^{2}}{5 y}$ and $\sqrt[3]{2}$ .

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