Simplify ( sixth root of 12x^5)/( sixth root of 2x^4)

$\frac{\sqrt[6]{12 x^{5}}}{\sqrt[6]{2 x^{4}}}$

Step 1

Combine $\sqrt[6]{12 x^{5}}$ and $\sqrt[6]{2 x^{4}}$ into a single radical.

$\sqrt[6]{\frac{12 x^{5}}{2 x^{4}}}$

Step 2

Reduce the expression $\frac{12 x^{5}}{2 x^{4}}$ by cancelling the common factors.

Factor $2$ out of $12 x^{5}$ .

$\sqrt[6]{\frac{2 (6 x^{5})}{2 x^{4}}}$

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

$\sqrt[6]{\frac{2 (6 x^{5})}{2 (x^{4})}}$

Cancel the common factor.

$\sqrt[6]{\frac{2 (6 x^{5})}{2 x^{4}}}$

Rewrite the expression.

$\sqrt[6]{\frac{6 x^{5}}{x^{4}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{4}$ .

Factor $x^{4}$ out of $6 x^{5}$ .

$\sqrt[6]{\frac{x^{4} (6 x)}{x^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[6]{\frac{x^{4} (6 x)}{x^{4} \cdot 1}}$

Cancel the common factor.

$\sqrt[6]{\frac{x^{4} (6 x)}{x^{4} \cdot 1}}$

Rewrite the expression.

$\sqrt[6]{\frac{6 x}{1}}$

Divide $6 x$ by $1$ .

$\sqrt[6]{6 x}$