Algebra Examples

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

Step 1

Combine $x$ and $\frac{2}{3}$ .

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

Step 2

Move $2$ to the left of $x$ .

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

Step 3

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

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

Step 4

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

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

Step 5

Combine and simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $2$ .

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

Step 5.5

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

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Step 5.5.1

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

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

Step 5.5.2

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

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

Step 5.5.3

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

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

Step 5.5.4

Cancel the common factor of $3$ .

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Step 5.5.4.1

Cancel the common factor.

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

Step 5.5.4.2

Rewrite the expression.

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

Step 5.5.5

Evaluate the exponent.

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

Step 6

Simplify the numerator.

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Step 6.1

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

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

Step 6.2

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

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

Step 7

Simplify the numerator.

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Step 7.1

Combine using the product rule for radicals.

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

Step 7.2

Multiply $9$ by $2$ .

$\frac{\sqrt[3]{18 x}}{3}$