Algebra Examples

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

Step 1

Combine $\sqrt[3]{2}$ and $\sqrt[3]{4 x^{2}}$ into a single radical.

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

Step 2

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

Tap for more steps...

Step 2.1

Factor $2$ out of $2$ .

$2 x \sqrt[3]{\frac{2 (1)}{4 x^{2}}}$

Step 2.2

Factor $2$ out of $4 x^{2}$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

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

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

Step 4

Any root of $1$ is $1$ .

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

Step 5

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

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

Step 6

Combine and simplify the denominator.

Tap for more steps...

Step 6.1

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

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

Step 6.2

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

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

Step 6.3

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

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

Step 6.4

Add $1$ and $2$ .

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

Step 6.5

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

Tap for more steps...

Step 6.5.1

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

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

Step 6.5.2

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

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

Step 6.5.3

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

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

Step 6.5.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.5.4.1

Cancel the common factor.

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

Step 6.5.4.2

Rewrite the expression.

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

Step 6.5.5

Simplify.

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

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

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

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

Step 7.2

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

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

Step 7.3

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

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

Step 7.4

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

Tap for more steps...

Step 7.4.1

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

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

Step 7.4.2

Multiply $2$ by $2$ .

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

Step 7.5

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

Tap for more steps...

Step 7.5.1

Factor out $x^{3}$ .

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

Step 7.5.2

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

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

Step 7.5.3

Add parentheses.

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

Step 7.6

Pull terms out from under the radical.

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

Step 8

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 8.1

Cancel the common factor of $2 x$ .

Tap for more steps...

Step 8.1.1

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

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

Step 8.1.2

Cancel the common factor.

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

Step 8.1.3

Rewrite the expression.

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

Step 8.2

Cancel the common factor of $x$ .

Tap for more steps...

Step 8.2.1

Cancel the common factor.

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

Step 8.2.2

Divide $\sqrt[3]{4 x}$ by $1$ .

$\sqrt[3]{4 x}$