Why do I get an imaginary result for the cube root of a negative number? I have a function that includes the phrase $(-x)^{1/3}$. It seems like this should always evaluate to $-(x^{1/3})$. For example, $-1 \cdot -1 \cdot -1 = -1$, so it seems that $(-1)^{1/3}$ should equal $-1$.
When I plug $(-1)^{(1/3)}$ into something like Mathematica, I get: 
0.5 + 0.866025i

Cubing this answer does in fact compute to $-1$.
Is this a situation, like $\sqrt4$, where there are two valid answers , $\{-2, 2\}$?

Use $e^{i\pi}=-1$. Then $(e^{i\pi})^{1/3}=e^{i\pi/3}=-1^{1/3}$
De Moivre's gives $e^{i\theta}=\cos(\theta)+i\sin(\theta)$
If $\theta=\frac{\pi}{3}$, then it follows that
$(-1)^{1/3}=e^{i(\pi/3)}=\frac12+\frac{i\sqrt3}{2}\approx0.5 + 0.866025i$
