Question

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

Answer 1

`root(6)2 = 2^(1/6)`

Explanation:

Well, 2 itself can be written as `2^1`, and the square root of two can be written as `sqrt2` and `sqrt2 * sqrt2` = 2, but alternatively `sqrt2` can be written as `2^(1/2)` and this works nicely because `2^(1/2) * 2^(1/2)` =2 and, as you recall, exponents add when multiplying the identical base.

Similarly `root(3)2` can be written as `2^(1/3)` and so `2^(1/3) * 2^(1/3) * 2^(1/3) = 2`

Carrying the same logic alone we see (I hope we do) `root(6)2` = `2^(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.