Algebra Examples

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

Step 1

Multiply $\frac{5 x}{\sqrt[3]{3 x^{2}}}$ by $\frac{{\sqrt[3]{3 x^{2}}}^{2}}{{\sqrt[3]{3 x^{2}}}^{2}}$ .

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

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

Add $1$ and $2$ .

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

Step 2.1.5

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

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Step 2.1.5.1

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

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

Step 2.1.5.2

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

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

Step 2.1.5.3

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

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

Step 2.1.5.4

Cancel the common factor of $3$ .

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Step 2.1.5.4.1

Cancel the common factor.

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

Step 2.1.5.4.2

Rewrite the expression.

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

Step 2.1.5.5

Simplify.

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

Step 2.2

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

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Step 2.2.1

Factor $x$ out of $5 x {\sqrt[3]{3 x^{2}}}^{2}$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x$ out of $3 x^{2}$ .

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 3

Simplify the numerator.

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Step 3.1

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

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

Step 3.2

Apply the product rule to $3 x^{2}$ .

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

Step 3.3

Raise $3$ to the power of $2$ .

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

Step 3.4

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

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Step 3.4.1

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

$\frac{5 \sqrt[3]{9 x^{2 \cdot 2}}}{3 x}$

Step 3.4.2

Multiply $2$ by $2$ .

$\frac{5 \sqrt[3]{9 x^{4}}}{3 x}$

Step 3.5

Rewrite $9 x^{4}$ as $x^{3} \cdot (9 x)$ .

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Step 3.5.1

Factor out $x^{3}$ .

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

Step 3.5.2

Reorder $9$ and $x^{3}$ .

$\frac{5 \sqrt[3]{x^{3} \cdot 9 x}}{3 x}$

Step 3.5.3

Add parentheses.

$\frac{5 \sqrt[3]{x^{3} \cdot (9 x)}}{3 x}$

Step 3.6

Pull terms out from under the radical.

$\frac{5 x \sqrt[3]{9 x}}{3 x}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\frac{5 x \sqrt[3]{9 x}}{3 x}$

Step 4.2

Rewrite the expression.

$\frac{5 \sqrt[3]{9 x}}{3}$