Algebra Examples

\sqrt[3]{\frac{108 x^{9} y^{10}}{2 x y^{3}}}

$\sqrt[3]{\frac{108 x^{9} y^{10}}{2 x y^{3}}}$

Step 1

Reduce the expression

\frac{108 x^{9} y^{10}}{2 x y^{3}}

$\frac{108 x^{9} y^{10}}{2 x y^{3}}$ by cancelling the common factors.

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Step 1.1

Factor

2

$2$ out of

108 x^{9} y^{10}

$108 x^{9} y^{10}$ .

\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 x y^{3}}}

$\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 x y^{3}}}$

Step 1.2

Factor

2

$2$ out of

2 x y^{3}

$2 x y^{3}$ .

\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 (x y^{3})}}

$\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 (x y^{3})}}$

Step 1.3

Cancel the common factor.

$\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 (x y^{3})}}$

Step 1.4

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{9} y^{10}}{x y^{3}}}$

Step 2

Cancel the common factor of

$x^{9}$ and

$x$ .

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Step 2.1

Factor

$x$ out of

$54 x^{9} y^{10}$ .

$\sqrt[3]{\frac{x (54 x^{8} y^{10})}{x y^{3}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

$x$ out of

$x y^{3}$ .

$\sqrt[3]{\frac{x (54 x^{8} y^{10})}{x (y^{3})}}$

Step 2.2.2

Cancel the common factor.

$\sqrt[3]{\frac{x (54 x^{8} y^{10})}{x y^{3}}}$

Step 2.2.3

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{8} y^{10}}{y^{3}}}$

Step 3

Cancel the common factor of

$y^{10}$ and

$y^{3}$ .

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Step 3.1

Factor

$y^{3}$ out of

$54 x^{8} y^{10}$ .

$\sqrt[3]{\frac{y^{3} (54 x^{8} y^{7})}{y^{3}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by

$1$ .

$\sqrt[3]{\frac{y^{3} (54 x^{8} y^{7})}{y^{3} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[3]{\frac{y^{3} (54 x^{8} y^{7})}{y^{3} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{8} y^{7}}{1}}$

Step 3.2.4

Divide

$54 x^{8} y^{7}$ by

$1$ .

$\sqrt[3]{54 x^{8} y^{7}}$

Step 4

Rewrite

$54 x^{8} y^{7}$ as

${(3 x^{2} y^{2})}^{3} \cdot (2 x^{2} y)$ .

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Step 4.1

Factor

$27$ out of

$54$ .

$\sqrt[3]{27 (2) x^{8} y^{7}}$

Step 4.2

Rewrite

$27$ as

$3^{3}$ .

$\sqrt[3]{3^{3} \cdot 2 x^{8} y^{7}}$

Step 4.3

Factor out

$x^{6}$ .

$\sqrt[3]{3^{3} \cdot 2 (x^{6} x^{2}) y^{7}}$

Step 4.4

Rewrite

$x^{6}$ as

${(x^{2})}^{3}$ .

$\sqrt[3]{3^{3} \cdot 2 ({(x^{2})}^{3} x^{2}) y^{7}}$

Step 4.5

Factor out

$y^{6}$ .

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

Step 4.6

Rewrite

$y^{6}$ as

${(y^{2})}^{3}$ .

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

Step 4.7

Move

$x^{2}$ .

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

Step 4.8

Move

$2$ .

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

Step 4.9

Rewrite

$(3^{3} ({(x^{2})}^{3})) {(y^{2})}^{3}$ as

${(3 x^{2} y^{2})}^{3}$ .

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

Step 4.10

Add parentheses.

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

Step 4.11

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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