Algebra Examples

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

Step 1

Factor out $m^{3}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $m$ by $m^{\frac{- 1}{2}}$ by adding the exponents.

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Step 3.1

Move $m^{\frac{- 1}{2}}$ .

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

Step 3.2

Multiply $m^{\frac{- 1}{2}}$ by $m$ .

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Move the negative in front of the fraction.

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

Step 3.4

Write $1$ as a fraction with a common denominator.

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

Step 3.5

Combine the numerators over the common denominator.

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

Step 3.6

Add $- 1$ and $2$ .

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

Step 4

Multiply $m^{\frac{1}{2}} \sqrt[3]{m}$ .

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Step 4.1

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

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

Step 4.2

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

$m^{\frac{1}{2} + \frac{1}{3}}$

Step 4.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4.4

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.5.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 4.5.2

Multiply $2$ by $3$ .

$m^{\frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2}}$

Step 4.5.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$m^{\frac{3}{6} + \frac{2}{3 \cdot 2}}$

Step 4.5.4

Multiply $3$ by $2$ .

$m^{\frac{3}{6} + \frac{2}{6}}$

Step 4.6

Combine the numerators over the common denominator.

$m^{\frac{3 + 2}{6}}$

Step 4.7

Add $3$ and $2$ .

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