I would like to confirm your answer, but the 2 different ways its written are unclear. I assume the problem you are trying to solve is:

2^[(1 + sqrt3) + (1 - sqrt3)] = 2^[2] = 4

OR

2^[(1 + sqrt3)*(1 - sqrt3)] = 2^[1 - 3] = 2^(-2) = 1/4

In either case, the answer is not 2