Algebra Examples

$\frac{9 \sqrt[5]{160 x^{8} y^{11}}}{3 \sqrt[5]{5 x y^{2}}}$

Step 1

Cancel the common factor of $9$ and $3$ .

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Step 1.1

Factor $3$ out of $9 \sqrt[5]{160 x^{8} y^{11}}$ .

$\frac{3 (3 \sqrt[5]{160 x^{8} y^{11}})}{3 \sqrt[5]{5 x y^{2}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3 \sqrt[5]{5 x y^{2}}$ .

$\frac{3 (3 \sqrt[5]{160 x^{8} y^{11}})}{3 (\sqrt[5]{5 x y^{2}})}$

Step 1.2.2

Cancel the common factor.

$\frac{3 (3 \sqrt[5]{160 x^{8} y^{11}})}{3 \sqrt[5]{5 x y^{2}}}$

Step 1.2.3

Rewrite the expression.

$\frac{3 \sqrt[5]{160 x^{8} y^{11}}}{\sqrt[5]{5 x y^{2}}}$

Step 2

Combine $\sqrt[5]{160 x^{8} y^{11}}$ and $\sqrt[5]{5 x y^{2}}$ into a single radical.

$3 \sqrt[5]{\frac{160 x^{8} y^{11}}{5 x y^{2}}}$

Step 3

Reduce the expression $\frac{160 x^{8} y^{11}}{5 x y^{2}}$ by cancelling the common factors.

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Step 3.1

Factor $5$ out of $160 x^{8} y^{11}$ .

$3 \sqrt[5]{\frac{5 (32 x^{8} y^{11})}{5 x y^{2}}}$

Step 3.2

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

$3 \sqrt[5]{\frac{5 (32 x^{8} y^{11})}{5 (x y^{2})}}$

Step 3.3

Cancel the common factor.

$3 \sqrt[5]{\frac{5 (32 x^{8} y^{11})}{5 (x y^{2})}}$

Step 3.4

Rewrite the expression.

$3 \sqrt[5]{\frac{32 x^{8} y^{11}}{x y^{2}}}$

Step 4

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

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Step 4.1

Factor $x$ out of $32 x^{8} y^{11}$ .

$3 \sqrt[5]{\frac{x (32 x^{7} y^{11})}{x y^{2}}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$3 \sqrt[5]{\frac{x (32 x^{7} y^{11})}{x (y^{2})}}$

Step 4.2.2

Cancel the common factor.

$3 \sqrt[5]{\frac{x (32 x^{7} y^{11})}{x y^{2}}}$

Step 4.2.3

Rewrite the expression.

$3 \sqrt[5]{\frac{32 x^{7} y^{11}}{y^{2}}}$

Step 5

Cancel the common factor of $y^{11}$ and $y^{2}$ .

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Step 5.1

Factor $y^{2}$ out of $32 x^{7} y^{11}$ .

$3 \sqrt[5]{\frac{y^{2} (32 x^{7} y^{9})}{y^{2}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$3 \sqrt[5]{\frac{y^{2} (32 x^{7} y^{9})}{y^{2} \cdot 1}}$

Step 5.2.2

Cancel the common factor.

$3 \sqrt[5]{\frac{y^{2} (32 x^{7} y^{9})}{y^{2} \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$3 \sqrt[5]{\frac{32 x^{7} y^{9}}{1}}$

Step 5.2.4

Divide $32 x^{7} y^{9}$ by $1$ .

$3 \sqrt[5]{32 x^{7} y^{9}}$

Step 6

Rewrite $32 x^{7} y^{9}$ as ${(2 x y)}^{5} (x^{2} y^{4})$ .

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Step 6.1

Rewrite $32$ as $2^{5}$ .

$3 \sqrt[5]{2^{5} x^{7} y^{9}}$

Step 6.2

Factor out $x^{5}$ .

$3 \sqrt[5]{2^{5} (x^{5} x^{2}) y^{9}}$

Step 6.3

Factor out $y^{5}$ .

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

Step 6.4

Move $x^{2}$ .

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

Step 6.5

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

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

Step 6.6

Add parentheses.

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

Step 7

Pull terms out from under the radical.

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

Step 8

Multiply $2$ by $3$ .

$6 x y \sqrt[5]{x^{2} y^{4}}$