Simplify ( cube root of 54x^5)/( cube root of 2x^2)

$\frac{\sqrt[3]{54 x^{5}}}{\sqrt[3]{2 x^{2}}}$

Combine $\sqrt[3]{54 x^{5}}$ and $\sqrt[3]{2 x^{2}}$ into a single radical.

$\sqrt[3]{\frac{54 x^{5}}{2 x^{2}}}$

Reduce the expression $\frac{54 x^{5}}{2 x^{2}}$ by cancelling the common factors.

Factor $2$ out of $54 x^{5}$ .

$\sqrt[3]{\frac{2 (27 x^{5})}{2 x^{2}}}$

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

$\sqrt[3]{\frac{2 (27 x^{5})}{2 (x^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (27 x^{5})}{2 x^{2}}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{5}}{x^{2}}}$

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $27 x^{5}$ .

$\sqrt[3]{\frac{x^{2} (27 x^{3})}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{2} (27 x^{3})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (27 x^{3})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{3}}{1}}$

Divide $27 x^{3}$ by $1$ .

$\sqrt[3]{27 x^{3}}$

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

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

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

$3 x$