Precalculus Examples

$\sqrt[4]{\frac{162 x^{4} y^{5}}{2 x^{8} y}}$

Step 1

Reduce the expression $\frac{162 x^{4} y^{5}}{2 x^{8} y}$ by cancelling the common factors.

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Step 1.1

Factor $2$ out of $162 x^{4} y^{5}$ .

$\sqrt[4]{\frac{2 (81 x^{4} y^{5})}{2 x^{8} y}}$

Step 1.2

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

$\sqrt[4]{\frac{2 (81 x^{4} y^{5})}{2 (x^{8} y)}}$

Step 1.3

Cancel the common factor.

$\sqrt[4]{\frac{2 (81 x^{4} y^{5})}{2 (x^{8} y)}}$

Step 1.4

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{4} y^{5}}{x^{8} y}}$

Step 2

Cancel the common factor of $x^{4}$ and $x^{8}$ .

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Step 2.1

Factor $x^{4}$ out of $81 x^{4} y^{5}$ .

$\sqrt[4]{\frac{x^{4} (81 y^{5})}{x^{8} y}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

$\sqrt[4]{\frac{x^{4} (81 y^{5})}{x^{4} (x^{4} y)}}$

Step 2.2.2

Cancel the common factor.

$\sqrt[4]{\frac{x^{4} (81 y^{5})}{x^{4} (x^{4} y)}}$

Step 2.2.3

Rewrite the expression.

$\sqrt[4]{\frac{81 y^{5}}{x^{4} y}}$

Step 3

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

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Step 3.1

Factor $y$ out of $81 y^{5}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Rewrite $81 y^{4}$ as ${(3 y)}^{4}$ .

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

Step 5

Rewrite $\frac{{(3 y)}^{4}}{x^{4}}$ as ${(\frac{3 y}{x})}^{4}$ .

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

Step 6

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

$\frac{3 y}{x}$