You would need 14 cases. You multiply 150 times 2 to get 300 which is 2 cases of soap per day and you multiply 7 days in a week by 2 and you let math magic happen
By DeMoivre's theorem,
(3 (cos(5<em>π</em>/6) + <em>i</em> sin(5<em>π</em>/6)))⁴ = 3⁴ (cos(4×5<em>π</em>/6) + <em>i</em> sin(4×5<em>π</em>/6))
… = 81 (cos(20<em>π</em>/6) + <em>i</em> sin(20<em>π</em>/6))
… = 81 (cos(10<em>π</em>/3) + <em>i</em> sin(10<em>π</em>/3))
… = 81 (cos(-2<em>π</em>/3) + <em>i</em> sin(-2<em>π</em>/3))
… = 81 (cos(2<em>π</em>/3) - <em>i</em> sin(2<em>π</em>/3))
… = 81 (-1/2 + √3/2 <em>i </em>)
… = -81/2 + 81√3/2 <em>i</em>
I've posted my answer together with the image I think this problem required.