Simplify ( cube root of 10)/( cube root of 625)

$\frac{\sqrt[3]{10}}{\sqrt[3]{625}}$

Combine $\sqrt[3]{10}$ and $\sqrt[3]{625}$ into a single radical.

$\sqrt[3]{\frac{10}{625}}$

Cancel the common factor of $10$ and $625$ .

Factor $5$ out of $10$ .

$\sqrt[3]{\frac{5 (2)}{625}}$

Cancel the common factors.

Factor $5$ out of $625$ .

$\sqrt[3]{\frac{5 \cdot 2}{5 \cdot 125}}$

Cancel the common factor.

$\sqrt[3]{\frac{5 \cdot 2}{5 \cdot 125}}$

Rewrite the expression.

$\sqrt[3]{\frac{2}{125}}$

Rewrite $\sqrt[3]{\frac{2}{125}}$ as $\frac{\sqrt[3]{2}}{\sqrt[3]{125}}$ .

$\frac{\sqrt[3]{2}}{\sqrt[3]{125}}$

Simplify the denominator.

Rewrite $125$ as $5^{3}$ .

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

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.25198420 \dots$