Divide ( fourth root of 12x^3)/( fourth root of 3x^2)

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

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.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $4 x$ by $1$ .

$\sqrt[4]{4 x}$