Algebra Examples

$\frac{\sqrt[3]{2 x^{5}}}{13}$

Step 1

Multiply to rationalize the numerator.

$\frac{\sqrt[3]{2 x^{5}} {\sqrt[3]{2 x^{5}}}^{2}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $\sqrt[3]{2 x^{5}}$ to the power of $1$ .

$\frac{{\sqrt[3]{2 x^{5}}}^{1} {\sqrt[3]{2 x^{5}}}^{2}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.2

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

$\frac{{\sqrt[3]{2 x^{5}}}^{1 + 2}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.3

Add $1$ and $2$ .

$\frac{{\sqrt[3]{2 x^{5}}}^{3}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.4

Rewrite ${\sqrt[3]{2 x^{5}}}^{3}$ as $2 x^{5}$ .

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Step 2.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x^{5}}$ as ${(2 x^{5})}^{\frac{1}{3}}$ .

$\frac{{({(2 x^{5})}^{\frac{1}{3}})}^{3}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.4.2

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

$\frac{{(2 x^{5})}^{\frac{1}{3} \cdot 3}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.4.3

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

$\frac{{(2 x^{5})}^{\frac{3}{3}}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.4.4

Cancel the common factor of $3$ .

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Step 2.4.4.1

Cancel the common factor.

$\frac{{(2 x^{5})}^{\frac{3}{3}}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.4.4.2

Rewrite the expression.

$\frac{{(2 x^{5})}^{1}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.4.5

Simplify.

$\frac{2 x^{5}}{13 {\sqrt[3]{2 x^{5}}}^{2}}$

Step 2.5

Start simplifying.

$\frac{2 x^{5}}{13 \sqrt[3]{{(2 x^{5})}^{2}}}$

Step 2.6

Apply the product rule to $2 x^{5}$ .

$\frac{2 x^{5}}{13 \sqrt[3]{2^{2} {(x^{5})}^{2}}}$

Step 2.7

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

$\frac{2 x^{5}}{13 \sqrt[3]{4 {(x^{5})}^{2}}}$

Step 2.8

Multiply the exponents in ${(x^{5})}^{2}$ .

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Step 2.8.1

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

$\frac{2 x^{5}}{13 \sqrt[3]{4 x^{5 \cdot 2}}}$

Step 2.8.2

Multiply $5$ by $2$ .

$\frac{2 x^{5}}{13 \sqrt[3]{4 x^{10}}}$

Step 2.9

Rewrite $4 x^{10}$ as ${(x^{3})}^{3} \cdot (4 x)$ .

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Step 2.9.1

Factor out $x^{9}$ .

$\frac{2 x^{5}}{13 \sqrt[3]{4 (x^{9} x)}}$

Step 2.9.2

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$\frac{2 x^{5}}{13 \sqrt[3]{4 ({(x^{3})}^{3} x)}}$

Step 2.9.3

Reorder $4$ and ${(x^{3})}^{3}$ .

$\frac{2 x^{5}}{13 \sqrt[3]{{(x^{3})}^{3} \cdot 4 x}}$

Step 2.9.4

Add parentheses.

$\frac{2 x^{5}}{13 \sqrt[3]{{(x^{3})}^{3} \cdot (4 x)}}$

Step 2.10

Pull terms out from under the radical.

$\frac{2 x^{5}}{13 x^{3} \sqrt[3]{4 x}}$