Answer
$z^4=625(cos~\frac{\pi}{3}+i~sin~\frac{\pi}{3})$
Work Step by Step
DeMoivre's Theorem:
If $z=r(cos~θ+i~sin~θ)$, then
$z^n=r^n(cos~nθ+i~sin~nθ)$
$z=5(cos~\frac{\pi}{12}+i~sin~\frac{\pi}{12})$
$z^4=5^4[cos~(4\frac{\pi}{12})+i~sin~(4\frac{\pi}{12})]$
$z^4=625(cos~\frac{\pi}{3}+i~sin~\frac{\pi}{3})$
