IMHO if it's for a senior engineer position, you should at least be able to explain how that would be implemented (bitwise operations) even if you wouldn't get it right in a whiteboard.
I know how bitwise operators works and have a CS degree... But even with googling I couldn't find a straight forward way to implement a general exponential operator using only bit operations.
Then, you need to code a multiply(x, y) method using some more bit shifting cleverness and your new add method.
Then, do repeated squaring using your new multiply method.
Aside from having to port an algorithm, I'm pretty sure the last time I used a bitwise operator seriously in 10 years was back in uni.
Unless this problem is for a job working on calculations on hardware that only supplies bitwise ops, it's a math trivia problem disguised as a coding interview question.