How do you simplify 10 /root3(4)?

Mar 18, 2018

see below.

Explanation:

First we need to find common factor between $10$ and $4$ and common factor between them are $2$
$\frac{10}{\sqrt[3]{4}} = \frac{2 \cdot 5}{\sqrt[3]{2} \cdot \sqrt[3]{2}}$

For this equation, we need to group $2$ into indices form.
$\frac{10}{\sqrt[3]{4}} = 5 \cdot \left(\frac{2}{\sqrt[3]{2}} ^ 2\right)$
$\frac{10}{\sqrt[3]{4}} = 5 \cdot \left(\frac{2}{2} ^ \left(\frac{2}{3}\right)\right)$
$\frac{10}{\sqrt[3]{4}} = 5 \cdot \left({2}^{1 - \frac{2}{3}}\right)$
$\frac{10}{\sqrt[3]{4}} = 5 \cdot {2}^{\frac{1}{3}}$

So the simplest form for $\frac{10}{\sqrt[3]{4}}$ is $5 \cdot {2}^{\frac{1}{3}}$.