Algebra Examples

$\frac{6}{\sqrt{4 y^{7}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $4 y^{7}$ as ${(2 y^{3})}^{2} y$ .

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Step 1.1.1

Rewrite $4$ as $2^{2}$ .

$\frac{6}{\sqrt{2^{2} y^{7}}}$

Step 1.1.2

Factor out $y^{6}$ .

$\frac{6}{\sqrt{2^{2} (y^{6} y)}}$

Step 1.1.3

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

$\frac{6}{\sqrt{2^{2} ({(y^{3})}^{2} y)}}$

Step 1.1.4

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

$\frac{6}{\sqrt{{(2 y^{3})}^{2} y}}$

Step 1.2

Pull terms out from under the radical.

$\frac{6}{2 y^{3} \sqrt{y}}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 3}{2 y^{3} \sqrt{y}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 y^{3} \sqrt{y}$ .

$\frac{2 \cdot 3}{2 (y^{3} \sqrt{y})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 \cdot 3}{2 (y^{3} \sqrt{y})}$

Step 2.2.3

Rewrite the expression.

$\frac{3}{y^{3} \sqrt{y}}$

Step 3

Multiply $\frac{3}{y^{3} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{3}{y^{3} \sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{3}{y^{3} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{3 \sqrt{y}}{y^{3} \sqrt{y} \sqrt{y}}$

Step 4.2

Move $\sqrt{y}$ .

$\frac{3 \sqrt{y}}{y^{3} (\sqrt{y} \sqrt{y})}$

Step 4.3

Raise $\sqrt{y}$ to the power of $1$ .

$\frac{3 \sqrt{y}}{y^{3} ({\sqrt{y}}^{1} \sqrt{y})}$

Step 4.4

Raise $\sqrt{y}$ to the power of $1$ .

$\frac{3 \sqrt{y}}{y^{3} ({\sqrt{y}}^{1} {\sqrt{y}}^{1})}$

Step 4.5

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

$\frac{3 \sqrt{y}}{y^{3} {\sqrt{y}}^{1 + 1}}$

Step 4.6

Add $1$ and $1$ .

$\frac{3 \sqrt{y}}{y^{3} {\sqrt{y}}^{2}}$

Step 4.7

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

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Step 4.7.1

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

$\frac{3 \sqrt{y}}{y^{3} {(y^{\frac{1}{2}})}^{2}}$

Step 4.7.2

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

$\frac{3 \sqrt{y}}{y^{3} y^{\frac{1}{2} \cdot 2}}$

Step 4.7.3

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

$\frac{3 \sqrt{y}}{y^{3} y^{\frac{2}{2}}}$

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

$\frac{3 \sqrt{y}}{y^{3} y^{\frac{2}{2}}}$

Step 4.7.4.2

Rewrite the expression.

$\frac{3 \sqrt{y}}{y^{3} y^{1}}$

Step 4.7.5

Simplify.

$\frac{3 \sqrt{y}}{y^{3} y}$

Step 5

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

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Step 5.1

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

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Step 5.1.1

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

$\frac{3 \sqrt{y}}{y^{3} y^{1}}$

Step 5.1.2

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

$\frac{3 \sqrt{y}}{y^{3 + 1}}$

Step 5.2

Add $3$ and $1$ .

$\frac{3 \sqrt{y}}{y^{4}}$