"use DeMoivre's theorem to find the indicated power of the complex number. Write the answer in rectangular form."

(squareroot{3(cos 5pie/6 + isin 5pie/6))^4

Am I doing this correctly?

(sqrt3)^4(cos(4*5pie/6)+isin(4*5pie/6)

9(cos 20pie/6)+isin(20pie/6)

9(-.5)+(-.866i)

=-4.5-7.8i

I'm worried I might have done this wrong due to the step in reducing 20pie/6 I couldn't find anything to reduce it by so just left it in that form.