I dont think its possible
Correction: I found the only solution, if a and b can be anything we cannot assume anything about their product (a*b). So x must be 1 for the result to have a to the first power. Therefore, x=1 will work.
*If you mean a+b in general
If you mean a Diophantine equation, there is a solution set [a=1, b=0, x=2,3,4,5...]. If you general a+b but value for x then there are no solutions.