Answer
$ \frac{27}{2}-\frac{27\sqrt 3}{2}i$
Work Step by Step
Based on the given conditions, we have:
$[\sqrt 3(cos\frac{5\pi}{18}+i\ sin\frac{5\pi}{18})]^6\\ =27(cos\frac{5\pi}{3}+i\ sin\frac{5\pi}{3})\\ =27(\frac{1}{2}-i\frac{\sqrt 3}{2})\\ =\frac{27}{2}-\frac{27\sqrt 3}{2}i$
