Basic Math Examples

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

Step 1

Factor out $n^{3}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

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

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Add $- 1$ and $2$ .

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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

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 $\frac{3}{3}$ .

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

Step 4.5.2

Multiply $2$ by $3$ .

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

Step 4.5.3

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

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

Step 4.5.4

Multiply $3$ by $2$ .

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

Step 4.6

Combine the numerators over the common denominator.

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

Step 4.7

Add $3$ and $2$ .

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