# How do you simplify (root6(8)*root6(16))/root6(2)?

Aug 26, 2016

$2$

#### Explanation:

Look for values you can cancel out:

write as:$\text{ } \frac{\sqrt[6]{\cancel{2} \times 4} \times \sqrt[6]{16}}{\cancel{\sqrt[6]{2}}}$

$\sqrt[6]{4 \times 16}$

$\sqrt[6]{64} = 2$

Aug 29, 2016

$2$

#### Explanation:

When we are multiplying or dividing with roots, we can combine them into one root. (as long as it is the same root in each case.)

$\frac{\sqrt[6]{8} \times \sqrt[6]{16}}{\sqrt[6]{2}}$

=$\sqrt[6]{\frac{8 \times 16}{2}}$

Simplifying gives: $\sqrt[6]{64}$

(It is very useful to know the powers of 2 up to ${2}^{10} = 1024$)

$\sqrt[6]{64} = \sqrt[6]{{2}^{6}}$

=$2$