Answer
$z^5=32(cos~\frac{4\pi}{3}+i~sin~\frac{4\pi}{3})$
Work Step by Step
DeMoivre's Theorem:
If $z=r(cos~θ+i~sin~θ)$, then
$z^n=r^n(cos~nθ+i~sin~nθ)$
$z=2(cos~\frac{4\pi}{15}+i~sin~\frac{4\pi}{15})$
$z^5=2^5[cos~(5\frac{4\pi}{15})+i~sin~(5\frac{4\pi}{15})]$
$z^5=32(cos~\frac{4\pi}{3}+i~sin~\frac{4\pi}{3})$
