Algebra Examples

$\sqrt[4]{\frac{405 x^{3} y^{3}}{5 x^{- 1} y}}$

Step 1

Reduce the expression $\frac{405 x^{3} y^{3}}{5 x^{- 1} y}$ by cancelling the common factors.

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Step 1.1

Factor $5$ out of $405 x^{3} y^{3}$ .

$\sqrt[4]{\frac{5 (81 x^{3} y^{3})}{5 x^{- 1} y}}$

Step 1.2

Factor $5$ out of $5 x^{- 1} y$ .

$\sqrt[4]{\frac{5 (81 x^{3} y^{3})}{5 (x^{- 1} y)}}$

Step 1.3

Cancel the common factor.

$\sqrt[4]{\frac{5 (81 x^{3} y^{3})}{5 (x^{- 1} y)}}$

Step 1.4

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{3} y^{3}}{x^{- 1} y}}$

Step 2

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[4]{\frac{81 x^{3} y^{3} x}{y}}$

Step 3

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

$\sqrt[4]{\frac{81 (x \cdot x^{3}) y^{3}}{y}}$

Step 3.2

Multiply $x$ by $x^{3}$ .

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Step 3.2.1

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

$\sqrt[4]{\frac{81 (x^{1} x^{3}) y^{3}}{y}}$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{\frac{81 x^{1 + 3} y^{3}}{y}}$

Step 3.3

Add $1$ and $3$ .

$\sqrt[4]{\frac{81 x^{4} y^{3}}{y}}$

Step 4

Cancel the common factor of $y^{3}$ and $y$ .

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Step 4.1

Factor $y$ out of $81 x^{4} y^{3}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y^{1}}}$

Step 4.2.2

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

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{4} y^{2}}{1}}$

Step 4.2.5

Divide $81 x^{4} y^{2}$ by $1$ .

$\sqrt[4]{81 x^{4} y^{2}}$

Step 5

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

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Remove non-negative terms from the absolute value.

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

Step 8

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$3 | x | \sqrt{\sqrt{y^{2}}}$

Step 9

Pull terms out from under the radical.

$3 | x | \sqrt{| y |}$