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

1 Answer
Reg H.
Dec 12, 2016

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.

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