# How do you simplify (root3(10))/(root3(32))?

Aug 24, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the expression as:

$\frac{\sqrt[3]{10}}{\sqrt[3]{8 \cdot 4}} \implies \frac{\sqrt[3]{10}}{\sqrt[3]{8} \sqrt[3]{4}} \implies \frac{\sqrt[3]{10}}{2 \sqrt[3]{4}}$

Next, we can rationalize the fraction by multiplying by the appropriate form of $1$:

$\frac{\sqrt[3]{2}}{\sqrt[3]{2}} \times \frac{\sqrt[3]{10}}{2 \sqrt[3]{4}} \implies$

$\frac{\sqrt[3]{2} \times \sqrt[3]{10}}{2 \sqrt[3]{4} \times \sqrt[3]{2}} \implies$

$\frac{\sqrt[3]{2 \times 10}}{2 \sqrt[3]{4 \times 2}} \implies$

$\frac{\sqrt[3]{20}}{2 \sqrt[3]{8}} \implies$

$\frac{\sqrt[3]{20}}{2 \times 2}$

$\frac{\sqrt[3]{20}}{4}$