Simplify ( cube root of 625x^4)/( cube root of 5x)

$\frac{\sqrt[3]{625 x^{4}}}{\sqrt[3]{5 x}}$

Combine $\sqrt[3]{625 x^{4}}$ and $\sqrt[3]{5 x}$ into a single radical.

$\sqrt[3]{\frac{625 x^{4}}{5 x}}$

Reduce the expression $\frac{625 x^{4}}{5 x}$ by cancelling the common factors.

Factor $5$ out of $625 x^{4}$ .

$\sqrt[3]{\frac{5 (125 x^{4})}{5 x}}$

Factor $5$ out of $5 x$ .

$\sqrt[3]{\frac{5 (125 x^{4})}{5 (x)}}$

Cancel the common factor.

$\sqrt[3]{\frac{5 (125 x^{4})}{5 x}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{4}}{x}}$

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

Factor $x$ out of $125 x^{4}$ .

$\sqrt[3]{\frac{x (125 x^{3})}{x}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{x (125 x^{3})}{x^{1}}}$

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

$\sqrt[3]{\frac{x (125 x^{3})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x (125 x^{3})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 x^{3}}{1}}$

Divide $125 x^{3}$ by $1$ .

$\sqrt[3]{125 x^{3}}$

Rewrite $125 x^{3}$ as ${(5 x)}^{3}$ .

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

Pull terms out from under the radical, assuming real numbers.

$5 x$