You have to be careful with your order of operations (associativity). Exponentiation first and then addition vs. addition first and then exponentiation. The exponentiation makes different operators, say:
eA = Ω and eB = Λ
Not only do you have to worry about A + B = B + A, which is almost trivial in a physics context, you must also worry about [Ω,Λ] = 0, which is often enough untrue.