Pre-Algebra Examples

$\frac{\sqrt[3]{432 x^{9} y \cdot 6}}{\sqrt[3]{2 y^{4}}}$

Step 1

Combine $\sqrt[3]{432 x^{9} y \cdot 6}$ and $\sqrt[3]{2 y^{4}}$ into a single radical.

$\sqrt[3]{\frac{432 x^{9} y \cdot 6}{2 y^{4}}}$

Step 2

Reduce the expression $\frac{432 x^{9} y \cdot 6}{2 y^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $2$ out of $432 x^{9} y \cdot 6$ .

$\sqrt[3]{\frac{2 (216 x^{9} y \cdot 6)}{2 y^{4}}}$

Step 2.2

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

$\sqrt[3]{\frac{2 (216 x^{9} y \cdot 6)}{2 (y^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt[3]{\frac{2 (216 x^{9} y \cdot 6)}{2 y^{4}}}$

Step 2.4

Rewrite the expression.

$\sqrt[3]{\frac{216 x^{9} y \cdot 6}{y^{4}}}$

Step 3

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

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Step 3.1

Factor $y$ out of $216 x^{9} y \cdot 6$ .

$\sqrt[3]{\frac{y (216 x^{9} \cdot 6)}{y^{4}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt[3]{\frac{y (216 x^{9} \cdot 6)}{y \cdot y^{3}}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y (216 x^{9} \cdot 6)}{y \cdot y^{3}}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{216 x^{9} \cdot 6}{y^{3}}}$

Step 4

Multiply $6$ by $216$ .

$\sqrt[3]{\frac{1296 x^{9}}{y^{3}}}$

Step 5

Rewrite $\frac{1296 x^{9}}{y^{3}}$ as ${(\frac{6 x^{3}}{y})}^{3} \cdot 6$ .

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Step 5.1

Factor the perfect power ${(6 x^{3})}^{3}$ out of $1296 x^{9}$ .

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

Step 5.2

Factor the perfect power $y^{3}$ out of $y^{3}$ .

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

Step 5.3

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

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

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