Question

how to evaluate roots of (1)^(1/8)

Answer 1

\(1^x=1\) for any number \(x\)

Answer 2

8th roots of unity?
You can use them complex number shinanigans and De'Moivre's Theorem to help you out.

Answer 3

Sorry, assumed real...

Answer 4

\[\large\rm 1=e^{0+2k \pi i}\]\[\large\rm 1^{1/8}=e^{\frac{2k \pi i}{8}}=e^{\frac{k \pi i}{4}}\]Consider the fist 8 integer values of k, starting from 0: k=0,1,2,3,4,5,6,7.
These will give us all our unique 8th roots of 1.
\(\large\rm e^{0}=1\)
\(\large\rm e^{\pi i/4}\)
I guess you'll have to convert to sines and cosines to simplify some of these roots :)

Answer 5

I can go into more detail if you need,
looks like you went offline for now though :D