Simplify cube root of (10x^5)/(54x^8)

$\sqrt[3]{\frac{10 x^{5}}{54 x^{8}}}$

Reduce the expression $\frac{10 x^{5}}{54 x^{8}}$ by cancelling the common factors.

Factor $2$ out of $10 x^{5}$ .

$\sqrt[3]{\frac{2 (5 x^{5})}{54 x^{8}}}$

Factor $2$ out of $54 x^{8}$ .

$\sqrt[3]{\frac{2 (5 x^{5})}{2 (27 x^{8})}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (5 x^{5})}{2 (27 x^{8})}}$

Rewrite the expression.

$\sqrt[3]{\frac{5 x^{5}}{27 x^{8}}}$

Cancel the common factor of $x^{5}$ and $x^{8}$ .

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

$\sqrt[3]{\frac{x^{5} \cdot 5}{27 x^{8}}}$

Cancel the common factors.

Factor $x^{5}$ out of $27 x^{8}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $\frac{5}{27 x^{3}}$ as ${(\frac{1}{3 x})}^{3} \cdot 5$ .

Factor the perfect power $1^{3}$ out of $5$ .

$\sqrt[3]{\frac{1^{3} \cdot 5}{27 x^{3}}}$

Factor the perfect power ${(3 x)}^{3}$ out of $27 x^{3}$ .

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

Rearrange the fraction $\frac{1^{3} \cdot 5}{{(3 x)}^{3} \cdot 1}$ .

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

Pull terms out from under the radical.

$\frac{1}{3 x} \sqrt[3]{5}$

Combine $\frac{1}{3 x}$ and $\sqrt[3]{5}$ .

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