Simplify the Radical Expression ( cube root of 4x^2)÷( cube root of x)

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

Rewrite the division as a fraction.

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

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

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

Reduce the expression by cancelling the common factors.

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

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

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

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

$\sqrt[3]{\frac{x (4 x)}{x^{1}}}$

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

$\sqrt[3]{\frac{x (4 x)}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x (4 x)}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{4 x}{1}}$

Divide $4 x$ by $1$ .

$\sqrt[3]{4 x}$