Why does x raised to an odd power result in a unique solution? I don't think I'm phrasing this correctly but anyway, say we are looking for solutions to x for $x^9=1/2$,
why is there only one unique solution as given by $x=(1/2)^{1/9}$
when by raising x to an even value gives two solutions as $\pm$ solution
I think I'm just missing a key concept so any help would be appreciated.

The simple answer is there is not only one solution, but only one real solution. For example, the equation $x^3=1$ has the solutions $x=1,e^{\frac{2i\pi}{3}},$ and $e^{\frac{4i\pi}{3}}$.
