# How do you write the expression root6(2) in exponential form?

Dec 12, 2016

$\sqrt[6]{2} = {2}^{\frac{1}{6}}$

#### Explanation:

Well, 2 itself can be written as ${2}^{1}$, and the square root of two can be written as $\sqrt{2}$ and $\sqrt{2} \cdot \sqrt{2}$ = 2, but alternatively $\sqrt{2}$ can be written as ${2}^{\frac{1}{2}}$ and this works nicely because ${2}^{\frac{1}{2}} \cdot {2}^{\frac{1}{2}}$ =2 and, as you recall, exponents add when multiplying the identical base.

Similarly $\sqrt[3]{2}$ can be written as ${2}^{\frac{1}{3}}$ and so ${2}^{\frac{1}{3}} \cdot {2}^{\frac{1}{3}} \cdot {2}^{\frac{1}{3}} = 2$

Carrying the same logic alone we see (I hope we do) $\sqrt[6]{2}$ = ${2}^{\frac{1}{6}}$

I am doing these basic questions to refresh my rusty skills, so, thank you.
if anyone can write this more elegantly, I welcome the assistance.