Algebra Examples

$\sqrt[3]{\frac{n}{4}} + \frac{n}{10}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt[3]{\frac{n}{4}}$ as $\frac{\sqrt[3]{n}}{\sqrt[3]{4}}$ .

$\frac{\sqrt[3]{n}}{\sqrt[3]{4}} + \frac{n}{10}$

Step 1.2

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

$\frac{\sqrt[3]{n}}{\sqrt[3]{4}} \cdot \frac{{\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{2}} + \frac{n}{10}$

Step 1.3

Combine and simplify the denominator.

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Step 1.3.1

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

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{\sqrt[3]{4} {\sqrt[3]{4}}^{2}} + \frac{n}{10}$

Step 1.3.2

Raise $\sqrt[3]{4}$ to the power of $1$ .

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{1} {\sqrt[3]{4}}^{2}} + \frac{n}{10}$

Step 1.3.3

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

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{1 + 2}} + \frac{n}{10}$

Step 1.3.4

Add $1$ and $2$ .

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{{\sqrt[3]{4}}^{3}} + \frac{n}{10}$

Step 1.3.5

Rewrite ${\sqrt[3]{4}}^{3}$ as $4$ .

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Step 1.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4}$ as $4^{\frac{1}{3}}$ .

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{{(4^{\frac{1}{3}})}^{3}} + \frac{n}{10}$

Step 1.3.5.2

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

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{4^{\frac{1}{3} \cdot 3}} + \frac{n}{10}$

Step 1.3.5.3

Combine $\frac{1}{3}$ and $3$ .

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{4^{\frac{3}{3}}} + \frac{n}{10}$

Step 1.3.5.4

Cancel the common factor of $3$ .

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Step 1.3.5.4.1

Cancel the common factor.

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{4^{\frac{3}{3}}} + \frac{n}{10}$

Step 1.3.5.4.2

Rewrite the expression.

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{4^{1}} + \frac{n}{10}$

Step 1.3.5.5

Evaluate the exponent.

$\frac{\sqrt[3]{n} {\sqrt[3]{4}}^{2}}{4} + \frac{n}{10}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Rewrite ${\sqrt[3]{4}}^{2}$ as $\sqrt[3]{4^{2}}$ .

$\frac{\sqrt[3]{n} \sqrt[3]{4^{2}}}{4} + \frac{n}{10}$

Step 1.4.2

Raise $4$ to the power of $2$ .

$\frac{\sqrt[3]{n} \sqrt[3]{16}}{4} + \frac{n}{10}$

Step 1.4.3

Rewrite $16$ as $2^{3} \cdot 2$ .

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Step 1.4.3.1

Factor $8$ out of $16$ .

$\frac{\sqrt[3]{n} \sqrt[3]{8 (2)}}{4} + \frac{n}{10}$

Step 1.4.3.2

Rewrite $8$ as $2^{3}$ .

$\frac{\sqrt[3]{n} \sqrt[3]{2^{3} \cdot 2}}{4} + \frac{n}{10}$

Step 1.4.4

Pull terms out from under the radical.

$\frac{\sqrt[3]{n} \cdot 2 \sqrt[3]{2}}{4} + \frac{n}{10}$

Step 1.4.5

Combine using the product rule for radicals.

$\frac{2 \sqrt[3]{n \cdot 2}}{4} + \frac{n}{10}$

Step 1.5

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

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Step 1.5.1

Factor $2$ out of $2 \sqrt[3]{n \cdot 2}$ .

$\frac{2 (\sqrt[3]{n \cdot 2})}{4} + \frac{n}{10}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $4$ .

$\frac{2 \sqrt[3]{n \cdot 2}}{2 \cdot 2} + \frac{n}{10}$

Step 1.5.2.2

Cancel the common factor.

$\frac{2 \sqrt[3]{n \cdot 2}}{2 \cdot 2} + \frac{n}{10}$

Step 1.5.2.3

Rewrite the expression.

$\frac{\sqrt[3]{n \cdot 2}}{2} + \frac{n}{10}$

Step 2

Reorder factors in $\frac{\sqrt[3]{n \cdot 2}}{2} + \frac{n}{10}$ .

$\frac{\sqrt[3]{2 n}}{2} + \frac{n}{10}$