Answer
$16*(-1/2+\sqrt 3*i)$
Work Step by Step
Let us first write the expression in cis notation,
We see that $1^2+(-\sqrt 3)^2=4$
Thus the magnitude of the polar number is 2.
Also from the unit circle, we recognize these values as 300 degrees
We can rewrite this as (degrees)
$(2cis(300))^4 = 2^4*cis(1200)=16*cis(120) = 16*(-1/2+\sqrt 3*i)$
