Algebra Examples

$\frac{4}{\sqrt[4]{8 m^{2}}}$

Step 1

Multiply $\frac{4}{\sqrt[4]{8 m^{2}}}$ by $\frac{{\sqrt[4]{8 m^{2}}}^{3}}{{\sqrt[4]{8 m^{2}}}^{3}}$ .

$\frac{4}{\sqrt[4]{8 m^{2}}} \cdot \frac{{\sqrt[4]{8 m^{2}}}^{3}}{{\sqrt[4]{8 m^{2}}}^{3}}$

Step 2

Simplify terms.

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Step 2.1

Combine and simplify the denominator.

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Step 2.1.1

Multiply $\frac{4}{\sqrt[4]{8 m^{2}}}$ by $\frac{{\sqrt[4]{8 m^{2}}}^{3}}{{\sqrt[4]{8 m^{2}}}^{3}}$ .

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{\sqrt[4]{8 m^{2}} {\sqrt[4]{8 m^{2}}}^{3}}$

Step 2.1.2

Raise $\sqrt[4]{8 m^{2}}$ to the power of $1$ .

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{\sqrt[4]{8 m^{2}}}^{1} {\sqrt[4]{8 m^{2}}}^{3}}$

Step 2.1.3

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

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{\sqrt[4]{8 m^{2}}}^{1 + 3}}$

Step 2.1.4

Add $1$ and $3$ .

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{\sqrt[4]{8 m^{2}}}^{4}}$

Step 2.1.5

Rewrite ${\sqrt[4]{8 m^{2}}}^{4}$ as $8 m^{2}$ .

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Step 2.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{8 m^{2}}$ as ${(8 m^{2})}^{\frac{1}{4}}$ .

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{({(8 m^{2})}^{\frac{1}{4}})}^{4}}$

Step 2.1.5.2

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

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{(8 m^{2})}^{\frac{1}{4} \cdot 4}}$

Step 2.1.5.3

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

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{(8 m^{2})}^{\frac{4}{4}}}$

Step 2.1.5.4

Cancel the common factor of $4$ .

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Step 2.1.5.4.1

Cancel the common factor.

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{(8 m^{2})}^{\frac{4}{4}}}$

Step 2.1.5.4.2

Rewrite the expression.

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{{(8 m^{2})}^{1}}$

Step 2.1.5.5

Simplify.

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{8 m^{2}}$

Step 2.2

Cancel the common factor of $4$ and $8$ .

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Step 2.2.1

Factor $4$ out of $4 {\sqrt[4]{8 m^{2}}}^{3}$ .

$\frac{4 ({\sqrt[4]{8 m^{2}}}^{3})}{8 m^{2}}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $4$ out of $8 m^{2}$ .

$\frac{4 ({\sqrt[4]{8 m^{2}}}^{3})}{4 (2 m^{2})}$

Step 2.2.2.2

Cancel the common factor.

$\frac{4 {\sqrt[4]{8 m^{2}}}^{3}}{4 (2 m^{2})}$

Step 2.2.2.3

Rewrite the expression.

$\frac{{\sqrt[4]{8 m^{2}}}^{3}}{2 m^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite ${\sqrt[4]{8 m^{2}}}^{3}$ as $\sqrt[4]{{(8 m^{2})}^{3}}$ .

$\frac{\sqrt[4]{{(8 m^{2})}^{3}}}{2 m^{2}}$

Step 3.2

Apply the product rule to $8 m^{2}$ .

$\frac{\sqrt[4]{8^{3} {(m^{2})}^{3}}}{2 m^{2}}$

Step 3.3

Raise $8$ to the power of $3$ .

$\frac{\sqrt[4]{512 {(m^{2})}^{3}}}{2 m^{2}}$

Step 3.4

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

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Step 3.4.1

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

$\frac{\sqrt[4]{512 m^{2 \cdot 3}}}{2 m^{2}}$

Step 3.4.2

Multiply $2$ by $3$ .

$\frac{\sqrt[4]{512 m^{6}}}{2 m^{2}}$

Step 3.5

Rewrite $512 m^{6}$ as ${(4 m)}^{4} \cdot (2 m^{2})$ .

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Step 3.5.1

Factor $256$ out of $512$ .

$\frac{\sqrt[4]{256 (2) m^{6}}}{2 m^{2}}$

Step 3.5.2

Rewrite $256$ as $4^{4}$ .

$\frac{\sqrt[4]{4^{4} \cdot 2 m^{6}}}{2 m^{2}}$

Step 3.5.3

Factor out $m^{4}$ .

$\frac{\sqrt[4]{4^{4} \cdot 2 (m^{4} m^{2})}}{2 m^{2}}$

Step 3.5.4

Move $2$ .

$\frac{\sqrt[4]{4^{4} m^{4} \cdot 2 m^{2}}}{2 m^{2}}$

Step 3.5.5

Rewrite $4^{4} m^{4}$ as ${(4 m)}^{4}$ .

$\frac{\sqrt[4]{{(4 m)}^{4} \cdot 2 m^{2}}}{2 m^{2}}$

Step 3.5.6

Add parentheses.

$\frac{\sqrt[4]{{(4 m)}^{4} \cdot (2 m^{2})}}{2 m^{2}}$

Step 3.6

Pull terms out from under the radical.

$\frac{4 m \sqrt[4]{2 m^{2}}}{2 m^{2}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

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

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Step 4.1.1

Factor $2$ out of $4 m \sqrt[4]{2 m^{2}}$ .

$\frac{2 (2 m \sqrt[4]{2 m^{2}})}{2 m^{2}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

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

$\frac{2 (2 m \sqrt[4]{2 m^{2}})}{2 (m^{2})}$

Step 4.1.2.2

Cancel the common factor.

$\frac{2 (2 m \sqrt[4]{2 m^{2}})}{2 m^{2}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{2 m \sqrt[4]{2 m^{2}}}{m^{2}}$

Step 4.2

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

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Step 4.2.1

Factor $m$ out of $2 m \sqrt[4]{2 m^{2}}$ .

$\frac{m (2 \sqrt[4]{2 m^{2}})}{m^{2}}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

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

$\frac{m (2 \sqrt[4]{2 m^{2}})}{m \cdot m}$

Step 4.2.2.2

Cancel the common factor.

$\frac{m (2 \sqrt[4]{2 m^{2}})}{m \cdot m}$

Step 4.2.2.3

Rewrite the expression.

$\frac{2 \sqrt[4]{2 m^{2}}}{m}$