Algebra Examples

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

Step 1

Multiply $\frac{\sqrt[3]{x \sqrt{y}}}{\sqrt[4]{x y^{2}}}$ by $\frac{{\sqrt[4]{x y^{2}}}^{3}}{{\sqrt[4]{x y^{2}}}^{3}}$ .

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

Step 2

Combine and simplify the denominator.

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Step 2.1

Multiply $\frac{\sqrt[3]{x \sqrt{y}}}{\sqrt[4]{x y^{2}}}$ by $\frac{{\sqrt[4]{x y^{2}}}^{3}}{{\sqrt[4]{x y^{2}}}^{3}}$ .

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

Step 2.2

Raise $\sqrt[4]{x y^{2}}$ to the power of $1$ .

$\frac{\sqrt[3]{x \sqrt{y}} {\sqrt[4]{x y^{2}}}^{3}}{{\sqrt[4]{x y^{2}}}^{1} {\sqrt[4]{x y^{2}}}^{3}}$

Step 2.3

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

$\frac{\sqrt[3]{x \sqrt{y}} {\sqrt[4]{x y^{2}}}^{3}}{{\sqrt[4]{x y^{2}}}^{1 + 3}}$

Step 2.4

Add $1$ and $3$ .

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

Step 2.5

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

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Step 2.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x y^{2}}$ as ${(x y^{2})}^{\frac{1}{4}}$ .

$\frac{\sqrt[3]{x \sqrt{y}} {\sqrt[4]{x y^{2}}}^{3}}{{({(x y^{2})}^{\frac{1}{4}})}^{4}}$

Step 2.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt[3]{x \sqrt{y}} {\sqrt[4]{x y^{2}}}^{3}}{{(x y^{2})}^{\frac{1}{4} \cdot 4}}$

Step 2.5.3

Combine $\frac{1}{4}$ and $4$ .

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

Step 2.5.4

Cancel the common factor of $4$ .

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Step 2.5.4.1

Cancel the common factor.

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

Step 2.5.4.2

Rewrite the expression.

$\frac{\sqrt[3]{x \sqrt{y}} {\sqrt[4]{x y^{2}}}^{3}}{{(x y^{2})}^{1}}$

Step 2.5.5

Simplify.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Apply the product rule to $x y^{2}$ .

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

Step 3.3

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 3.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 3.3.2

Multiply $2$ by $3$ .

$\frac{\sqrt[3]{x \sqrt{y}} \sqrt[4]{x^{3} y^{6}}}{x y^{2}}$

Step 3.4

Rewrite $x^{3} y^{6}$ as $y^{4} (x^{3} y^{2})$ .

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Step 3.4.1

Factor out $y^{4}$ .

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

Step 3.4.2

Reorder $x^{3}$ and $y^{4}$ .

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

Step 3.4.3

Add parentheses.

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

Step 3.5

Pull terms out from under the radical.

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

Step 3.6

Combine exponents.

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Step 3.6.1

Rewrite the expression using the least common index of $12$ .

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Step 3.6.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x \sqrt{y}}$ as ${(x \sqrt{y})}^{\frac{1}{3}}$ .

$\frac{y ({(x \sqrt{y})}^{\frac{1}{3}} \sqrt[4]{x^{3} y^{2}})}{x y^{2}}$

Step 3.6.1.2

Rewrite ${(x \sqrt{y})}^{\frac{1}{3}}$ as ${(x \sqrt{y})}^{\frac{4}{12}}$ .

$\frac{y ({(x \sqrt{y})}^{\frac{4}{12}} \sqrt[4]{x^{3} y^{2}})}{x y^{2}}$

Step 3.6.1.3

Rewrite ${(x \sqrt{y})}^{\frac{4}{12}}$ as $\sqrt[12]{{(x \sqrt{y})}^{4}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} \sqrt[4]{x^{3} y^{2}})}{x y^{2}}$

Step 3.6.1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{3} y^{2}}$ as ${(x^{3} y^{2})}^{\frac{1}{4}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} {(x^{3} y^{2})}^{\frac{1}{4}})}{x y^{2}}$

Step 3.6.1.5

Rewrite ${(x^{3} y^{2})}^{\frac{1}{4}}$ as ${(x^{3} y^{2})}^{\frac{3}{12}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} {(x^{3} y^{2})}^{\frac{3}{12}})}{x y^{2}}$

Step 3.6.1.6

Rewrite ${(x^{3} y^{2})}^{\frac{3}{12}}$ as $\sqrt[12]{{(x^{3} y^{2})}^{3}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} \sqrt[12]{{(x^{3} y^{2})}^{3}})}{x y^{2}}$

Step 3.6.2

Combine using the product rule for radicals.

$\frac{y \sqrt[12]{{(x \sqrt{y})}^{4} {(x^{3} y^{2})}^{3}}}{x y^{2}}$

Step 3.6.3

Apply the product rule to $x \sqrt{y}$ .

$\frac{y \sqrt[12]{x^{4} {\sqrt{y}}^{4} {(x^{3} y^{2})}^{3}}}{x y^{2}}$

Step 3.6.4

Apply the product rule to $x^{3} y^{2}$ .

$\frac{y \sqrt[12]{x^{4} {\sqrt{y}}^{4} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5

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

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Step 3.6.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\frac{y \sqrt[12]{x^{4} {(y^{\frac{1}{2}})}^{4} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{1}{2} \cdot 4} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.3

Combine $\frac{1}{2}$ and $4$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{4}{2}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.4

Cancel the common factor of $4$ and $2$ .

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Step 3.6.5.4.1

Factor $2$ out of $4$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{2 \cdot 2}{2}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.4.2

Cancel the common factors.

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Step 3.6.5.4.2.1

Factor $2$ out of $2$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{2 \cdot 2}{2 (1)}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.4.2.2

Cancel the common factor.

$\frac{y \sqrt[12]{x^{4} y^{\frac{2 \cdot 2}{2 \cdot 1}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.4.2.3

Rewrite the expression.

$\frac{y \sqrt[12]{x^{4} y^{\frac{2}{1}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.5.4.2.4

Divide $2$ by $1$ .

$\frac{y \sqrt[12]{x^{4} y^{2} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.6

Multiply the exponents in ${(x^{3})}^{3}$ .

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Step 3.6.6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{3 \cdot 3} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.6.2

Multiply $3$ by $3$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{9} {(y^{2})}^{3}}}{x y^{2}}$

Step 3.6.7

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 3.6.7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{9} y^{2 \cdot 3}}}{x y^{2}}$

Step 3.6.7.2

Multiply $2$ by $3$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{9} y^{6}}}{x y^{2}}$

Step 3.6.8

Combine exponents.

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Step 3.6.8.1

Multiply $x^{4}$ by $x^{9}$ by adding the exponents.

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Step 3.6.8.1.1

Move $x^{9}$ .

$\frac{y \sqrt[12]{x^{9} x^{4} y^{2} y^{6}}}{x y^{2}}$

Step 3.6.8.1.2

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

$\frac{y \sqrt[12]{x^{9 + 4} y^{2} y^{6}}}{x y^{2}}$

Step 3.6.8.1.3

Add $9$ and $4$ .

$\frac{y \sqrt[12]{x^{13} y^{2} y^{6}}}{x y^{2}}$

Step 3.6.8.2

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 3.6.8.2.1

Move $y^{6}$ .

$\frac{y \sqrt[12]{x^{13} (y^{6} y^{2})}}{x y^{2}}$

Step 3.6.8.2.2

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

$\frac{y \sqrt[12]{x^{13} y^{6 + 2}}}{x y^{2}}$

Step 3.6.8.2.3

Add $6$ and $2$ .

$\frac{y \sqrt[12]{x^{13} y^{8}}}{x y^{2}}$

Step 3.7

Rewrite $x^{13} y^{8}$ as $x^{12} (x y^{8})$ .

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Step 3.7.1

Factor out $x^{12}$ .

$\frac{y \sqrt[12]{x^{12} x y^{8}}}{x y^{2}}$

Step 3.7.2

Add parentheses.

$\frac{y \sqrt[12]{x^{12} (x y^{8})}}{x y^{2}}$

Step 3.8

Pull terms out from under the radical.

$\frac{y (x \sqrt[12]{x y^{8}})}{x y^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Rewrite.

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

Step 4.2

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

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

Step 4.3

Apply the product rule to $x y^{2}$ .

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

Step 4.4

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 4.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.4.2

Multiply $2$ by $3$ .

$\frac{\sqrt[3]{x \sqrt{y}} \sqrt[4]{x^{3} y^{6}}}{x y^{2}}$

Step 4.5

Rewrite $x^{3} y^{6}$ as $y^{4} (x^{3} y^{2})$ .

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Step 4.5.1

Factor out $y^{4}$ .

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

Step 4.5.2

Reorder $x^{3}$ and $y^{4}$ .

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

Step 4.5.3

Add parentheses.

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

Step 4.6

Pull terms out from under the radical.

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

Step 4.7

Combine exponents.

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Step 4.7.1

Rewrite the expression using the least common index of $12$ .

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Step 4.7.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x \sqrt{y}}$ as ${(x \sqrt{y})}^{\frac{1}{3}}$ .

$\frac{y ({(x \sqrt{y})}^{\frac{1}{3}} \sqrt[4]{x^{3} y^{2}})}{x y^{2}}$

Step 4.7.1.2

Rewrite ${(x \sqrt{y})}^{\frac{1}{3}}$ as ${(x \sqrt{y})}^{\frac{4}{12}}$ .

$\frac{y ({(x \sqrt{y})}^{\frac{4}{12}} \sqrt[4]{x^{3} y^{2}})}{x y^{2}}$

Step 4.7.1.3

Rewrite ${(x \sqrt{y})}^{\frac{4}{12}}$ as $\sqrt[12]{{(x \sqrt{y})}^{4}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} \sqrt[4]{x^{3} y^{2}})}{x y^{2}}$

Step 4.7.1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{3} y^{2}}$ as ${(x^{3} y^{2})}^{\frac{1}{4}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} {(x^{3} y^{2})}^{\frac{1}{4}})}{x y^{2}}$

Step 4.7.1.5

Rewrite ${(x^{3} y^{2})}^{\frac{1}{4}}$ as ${(x^{3} y^{2})}^{\frac{3}{12}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} {(x^{3} y^{2})}^{\frac{3}{12}})}{x y^{2}}$

Step 4.7.1.6

Rewrite ${(x^{3} y^{2})}^{\frac{3}{12}}$ as $\sqrt[12]{{(x^{3} y^{2})}^{3}}$ .

$\frac{y (\sqrt[12]{{(x \sqrt{y})}^{4}} \sqrt[12]{{(x^{3} y^{2})}^{3}})}{x y^{2}}$

Step 4.7.2

Combine using the product rule for radicals.

$\frac{y \sqrt[12]{{(x \sqrt{y})}^{4} {(x^{3} y^{2})}^{3}}}{x y^{2}}$

Step 4.7.3

Apply the product rule to $x \sqrt{y}$ .

$\frac{y \sqrt[12]{x^{4} {\sqrt{y}}^{4} {(x^{3} y^{2})}^{3}}}{x y^{2}}$

Step 4.7.4

Apply the product rule to $x^{3} y^{2}$ .

$\frac{y \sqrt[12]{x^{4} {\sqrt{y}}^{4} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5

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

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Step 4.7.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\frac{y \sqrt[12]{x^{4} {(y^{\frac{1}{2}})}^{4} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{1}{2} \cdot 4} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.3

Combine $\frac{1}{2}$ and $4$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{4}{2}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.4

Cancel the common factor of $4$ and $2$ .

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Step 4.7.5.4.1

Factor $2$ out of $4$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{2 \cdot 2}{2}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.4.2

Cancel the common factors.

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Step 4.7.5.4.2.1

Factor $2$ out of $2$ .

$\frac{y \sqrt[12]{x^{4} y^{\frac{2 \cdot 2}{2 (1)}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.4.2.2

Cancel the common factor.

$\frac{y \sqrt[12]{x^{4} y^{\frac{2 \cdot 2}{2 \cdot 1}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.4.2.3

Rewrite the expression.

$\frac{y \sqrt[12]{x^{4} y^{\frac{2}{1}} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.5.4.2.4

Divide $2$ by $1$ .

$\frac{y \sqrt[12]{x^{4} y^{2} {(x^{3})}^{3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.6

Multiply the exponents in ${(x^{3})}^{3}$ .

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Step 4.7.6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{3 \cdot 3} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.6.2

Multiply $3$ by $3$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{9} {(y^{2})}^{3}}}{x y^{2}}$

Step 4.7.7

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 4.7.7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{9} y^{2 \cdot 3}}}{x y^{2}}$

Step 4.7.7.2

Multiply $2$ by $3$ .

$\frac{y \sqrt[12]{x^{4} y^{2} x^{9} y^{6}}}{x y^{2}}$

Step 4.7.8

Combine exponents.

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Step 4.7.8.1

Multiply $x^{4}$ by $x^{9}$ by adding the exponents.

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Step 4.7.8.1.1

Move $x^{9}$ .

$\frac{y \sqrt[12]{x^{9} x^{4} y^{2} y^{6}}}{x y^{2}}$

Step 4.7.8.1.2

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

$\frac{y \sqrt[12]{x^{9 + 4} y^{2} y^{6}}}{x y^{2}}$

Step 4.7.8.1.3

Add $9$ and $4$ .

$\frac{y \sqrt[12]{x^{13} y^{2} y^{6}}}{x y^{2}}$

Step 4.7.8.2

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

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Step 4.7.8.2.1

Move $y^{6}$ .

$\frac{y \sqrt[12]{x^{13} (y^{6} y^{2})}}{x y^{2}}$

Step 4.7.8.2.2

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

$\frac{y \sqrt[12]{x^{13} y^{6 + 2}}}{x y^{2}}$

Step 4.7.8.2.3

Add $6$ and $2$ .

$\frac{y \sqrt[12]{x^{13} y^{8}}}{x y^{2}}$

Step 4.8

Rewrite $x^{13} y^{8}$ as $x^{12} (x y^{8})$ .

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Step 4.8.1

Factor out $x^{12}$ .

$\frac{y \sqrt[12]{x^{12} x y^{8}}}{x y^{2}}$

Step 4.8.2

Add parentheses.

$\frac{y \sqrt[12]{x^{12} (x y^{8})}}{x y^{2}}$

Step 4.9

Pull terms out from under the radical.

$\frac{y (x \sqrt[12]{x y^{8}})}{x y^{2}}$

Step 4.10

Remove unnecessary parentheses.

$\frac{y x \sqrt[12]{x y^{8}}}{x y^{2}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

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

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Step 5.1.1

Factor $y$ out of $y x \sqrt[12]{x y^{8}}$ .

$\frac{y (x \sqrt[12]{x y^{8}})}{x y^{2}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

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

$\frac{y (x \sqrt[12]{x y^{8}})}{y (x y)}$

Step 5.1.2.2

Cancel the common factor.

$\frac{y (x \sqrt[12]{x y^{8}})}{y (x y)}$

Step 5.1.2.3

Rewrite the expression.

$\frac{x \sqrt[12]{x y^{8}}}{x y}$

Step 5.2

Cancel the common factor of $x$ .

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Step 5.2.1

Cancel the common factor.

$\frac{x \sqrt[12]{x y^{8}}}{x y}$

Step 5.2.2

Rewrite the expression.

$\frac{\sqrt[12]{x y^{8}}}{y}$