Simplify ( cube root of 10x^2)/( cube root of 2x^8)

$\frac{\sqrt[3]{10 x^{2}}}{\sqrt[3]{2 x^{8}}}$

Combine $\sqrt[3]{10 x^{2}}$ and $\sqrt[3]{2 x^{8}}$ into a single radical.

$\sqrt[3]{\frac{10 x^{2}}{2 x^{8}}}$

Reduce the expression $\frac{10 x^{2}}{2 x^{8}}$ by cancelling the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x^{2}$ and $x^{8}$ .

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

$\sqrt[3]{\frac{x^{2} \cdot 5}{x^{8}}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{x^{2} \cdot 5}{x^{2} x^{6}}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} \cdot 5}{x^{2} x^{6}}}$

Rewrite the expression.

$\sqrt[3]{\frac{5}{x^{6}}}$

Rewrite $\frac{5}{x^{6}}$ as ${(\frac{1}{x^{2}})}^{3} \cdot 5$ .

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

$\sqrt[3]{\frac{1^{3} \cdot 5}{x^{6}}}$

Factor the perfect power ${(x^{2})}^{3}$ out of $x^{6}$ .

$\sqrt[3]{\frac{1^{3} \cdot 5}{{(x^{2})}^{3} \cdot 1}}$

Rearrange the fraction $\frac{1^{3} \cdot 5}{{(x^{2})}^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{1}{x^{2}})}^{3} \cdot 5}$

Pull terms out from under the radical.

$\frac{1}{x^{2}} \sqrt[3]{5}$

Combine $\frac{1}{x^{2}}$ and $\sqrt[3]{5}$ .

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