Simplify ( fifth root of 15x^4)/( fifth root of 3x^3)

$\frac{\sqrt[5]{15 x^{4}}}{\sqrt[5]{3 x^{3}}}$

Step 1

Combine $\sqrt[5]{15 x^{4}}$ and $\sqrt[5]{3 x^{3}}$ into a single radical.

$\sqrt[5]{\frac{15 x^{4}}{3 x^{3}}}$

Step 2

Reduce the expression $\frac{15 x^{4}}{3 x^{3}}$ by cancelling the common factors.

Factor $3$ out of $15 x^{4}$ .

$\sqrt[5]{\frac{3 (5 x^{4})}{3 x^{3}}}$

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

$\sqrt[5]{\frac{3 (5 x^{4})}{3 (x^{3})}}$

Cancel the common factor.

$\sqrt[5]{\frac{3 (5 x^{4})}{3 x^{3}}}$

Rewrite the expression.

$\sqrt[5]{\frac{5 x^{4}}{x^{3}}}$

Step 3

Cancel the common factor of $x^{4}$ and $x^{3}$ .

Factor $x^{3}$ out of $5 x^{4}$ .

$\sqrt[5]{\frac{x^{3} (5 x)}{x^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[5]{\frac{x^{3} (5 x)}{x^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt[5]{\frac{x^{3} (5 x)}{x^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt[5]{\frac{5 x}{1}}$

Divide $5 x$ by $1$ .

$\sqrt[5]{5 x}$