Complexity of generating power sets
Complexity time $O(2^n)$ is called $\text{DTIME}(O(2^n))$ and is a sub-complexity class of E which is in turn a sub-complexity class of EXPTIME.
To prove you can do it within $O(2^n)$ time, you have to provide an algorithm for that and show the algorithm runs in no more than $O(2^n)$.