The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.
If $\displaystyle \alpha\in\mathbb{R}$, a real number, then if
$\displaystyle z=\frac{1}{2}+\frac{\sqrt{3}}{2}i=\exp\left(\frac{ i\pi}{3}\right)$ we have
$\displaystyle z^{\alpha}=\exp\left(\frac{i\pi\alpha}{3}\right)$.