Pre-Algebra Examples

$\frac{\sqrt[4]{486 x^{12} y^{22}}}{\sqrt[4]{6 x^{4} y}}$

Step 1

Combine $\sqrt[4]{486 x^{12} y^{22}}$ and $\sqrt[4]{6 x^{4} y}$ into a single radical.

$\sqrt[4]{\frac{486 x^{12} y^{22}}{6 x^{4} y}}$

Step 2

Reduce the expression $\frac{486 x^{12} y^{22}}{6 x^{4} y}$ by cancelling the common factors.

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Step 2.1

Factor $6$ out of $486 x^{12} y^{22}$ .

$\sqrt[4]{\frac{6 (81 x^{12} y^{22})}{6 x^{4} y}}$

Step 2.2

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

$\sqrt[4]{\frac{6 (81 x^{12} y^{22})}{6 (x^{4} y)}}$

Step 2.3

Cancel the common factor.

$\sqrt[4]{\frac{6 (81 x^{12} y^{22})}{6 (x^{4} y)}}$

Step 2.4

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{12} y^{22}}{x^{4} y}}$

Step 3

Cancel the common factor of $x^{12}$ and $x^{4}$ .

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Step 3.1

Factor $x^{4}$ out of $81 x^{12} y^{22}$ .

$\sqrt[4]{\frac{x^{4} (81 x^{8} y^{22})}{x^{4} y}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt[4]{\frac{x^{4} (81 x^{8} y^{22})}{x^{4} (y)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[4]{\frac{x^{4} (81 x^{8} y^{22})}{x^{4} y}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{8} y^{22}}{y}}$

Step 4

Cancel the common factor of $y^{22}$ and $y$ .

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Step 4.1

Factor $y$ out of $81 x^{8} y^{22}$ .

$\sqrt[4]{\frac{y (81 x^{8} y^{21})}{y}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\sqrt[4]{\frac{y (81 x^{8} y^{21})}{y^{1}}}$

Step 4.2.2

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

$\sqrt[4]{\frac{y (81 x^{8} y^{21})}{y \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$\sqrt[4]{\frac{y (81 x^{8} y^{21})}{y \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{8} y^{21}}{1}}$

Step 4.2.5

Divide $81 x^{8} y^{21}$ by $1$ .

$\sqrt[4]{81 x^{8} y^{21}}$

Step 5

Rewrite $81 x^{8} y^{21}$ as ${(3 x^{2} y^{5})}^{4} y$ .

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Step 5.1

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} x^{8} y^{21}}$

Step 5.2

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

$\sqrt[4]{3^{4} {(x^{2})}^{4} y^{21}}$

Step 5.3

Factor out $y^{20}$ .

$\sqrt[4]{3^{4} {(x^{2})}^{4} (y^{20} y)}$

Step 5.4

Rewrite $y^{20}$ as ${(y^{5})}^{4}$ .

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

Step 5.5

Rewrite $3^{4} {(x^{2})}^{4} {(y^{5})}^{4}$ as ${(3 x^{2} y^{5})}^{4}$ .

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

Step 6

Pull terms out from under the radical.

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