Algebra Examples

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

Step 1

Reduce the expression $\frac{2 x}{4}$ by cancelling the common factors.

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Step 1.1

Factor $2$ out of $2 x$ .

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

Step 1.2

Factor $2$ out of $4$ .

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

Combine and simplify the denominator.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $2$ .

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

Step 4.5

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

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Step 4.5.1

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

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

Step 4.5.2

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

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

Step 4.5.3

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

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

Step 4.5.4

Cancel the common factor of $3$ .

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Step 4.5.4.1

Cancel the common factor.

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

Step 4.5.4.2

Rewrite the expression.

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

Step 4.5.5

Evaluate the exponent.

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

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Combine using the product rule for radicals.

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

Step 7

Reorder factors in $\frac{\sqrt[3]{x \cdot 4}}{2}$ .

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