Algebra Examples

$\frac{2 m^{2}}{\sqrt{36 m^{11}}}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $36 m^{11}$ as ${(6 m^{5})}^{2} m$ .

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Step 1.1.1

Rewrite $36$ as $6^{2}$ .

$\frac{2 m^{2}}{\sqrt{6^{2} m^{11}}}$

Step 1.1.2

Factor out $m^{10}$ .

$\frac{2 m^{2}}{\sqrt{6^{2} (m^{10} m)}}$

Step 1.1.3

Rewrite $m^{10}$ as ${(m^{5})}^{2}$ .

$\frac{2 m^{2}}{\sqrt{6^{2} ({(m^{5})}^{2} m)}}$

Step 1.1.4

Rewrite $6^{2} {(m^{5})}^{2}$ as ${(6 m^{5})}^{2}$ .

$\frac{2 m^{2}}{\sqrt{{(6 m^{5})}^{2} m}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2 m^{2}}{6 m^{5} \sqrt{m}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

Factor $2$ out of $2 m^{2}$ .

$\frac{2 (m^{2})}{6 m^{5} \sqrt{m}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $6 m^{5} \sqrt{m}$ .

$\frac{2 (m^{2})}{2 (3 m^{5} \sqrt{m})}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 m^{2}}{2 (3 m^{5} \sqrt{m})}$

Step 2.1.2.3

Rewrite the expression.

$\frac{m^{2}}{3 m^{5} \sqrt{m}}$

Step 2.2

Cancel the common factor of $m^{2}$ and $m^{5}$ .

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Step 2.2.1

Multiply by $1$ .

$\frac{m^{2} \cdot 1}{3 m^{5} \sqrt{m}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $m^{2}$ out of $3 m^{5} \sqrt{m}$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 3

Multiply $\frac{1}{3 m^{3} \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

$\frac{1}{3 m^{3} \sqrt{m}} \cdot \frac{\sqrt{m}}{\sqrt{m}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{1}{3 m^{3} \sqrt{m}}$ by $\frac{\sqrt{m}}{\sqrt{m}}$ .

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

Step 4.2

Move $\sqrt{m}$ .

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

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

Step 4.6

Add $1$ and $1$ .

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

Step 4.7

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

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Step 4.7.1

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

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

Step 4.7.2

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

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

Step 4.7.3

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

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

Step 4.7.4

Cancel the common factor of $2$ .

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Step 4.7.4.1

Cancel the common factor.

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

Step 4.7.4.2

Rewrite the expression.

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

Step 4.7.5

Simplify.

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

Step 5

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

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Step 5.1

Move $m$ .

$\frac{\sqrt{m}}{3 (m \cdot m^{3})}$

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

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

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

Step 5.3

Add $1$ and $3$ .

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