Algebra Examples

$\frac{\sqrt[4]{12 x^{3}}}{\sqrt[4]{3 x^{2}}}$

Step 1

Combine $\sqrt[4]{12 x^{3}}$ and $\sqrt[4]{3 x^{2}}$ into a single radical.

$\sqrt[4]{\frac{12 x^{3}}{3 x^{2}}}$

Step 2

Reduce the expression $\frac{12 x^{3}}{3 x^{2}}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $12 x^{3}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 3.1

Factor $x^{2}$ out of $4 x^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\sqrt[4]{\frac{4 x}{1}}$

Step 3.2.4

Divide $4 x$ by $1$ .

$\sqrt[4]{4 x}$