Simplify ( cube root of 15x^2)/( cube root of 5x)

$\frac{\sqrt[3]{15 x^{2}}}{\sqrt[3]{5 x}}$

Step 1

Combine $\sqrt[3]{15 x^{2}}$ and $\sqrt[3]{5 x}$ into a single radical.

$\sqrt[3]{\frac{15 x^{2}}{5 x}}$

Step 2

Reduce the expression $\frac{15 x^{2}}{5 x}$ by cancelling the common factors.

Factor $5$ out of $15 x^{2}$ .

$\sqrt[3]{\frac{5 (3 x^{2})}{5 x}}$

Factor $5$ out of $5 x$ .

$\sqrt[3]{\frac{5 (3 x^{2})}{5 (x)}}$

Cancel the common factor.

$\sqrt[3]{\frac{5 (3 x^{2})}{5 x}}$

Rewrite the expression.

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

Step 3

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

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

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

Cancel the common factors.

Raise $x$ to the power of $1$ .

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

Factor $x$ out of $x^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 x$ by $1$ .

$\sqrt[3]{3 x}$