Is it possible to simplify $O(A \times B \times C + A^B)$ into $O(A^B)$
No, it is not possible. The function $ABC$ is $O(ABC + A^B)$ but not $A^B$, since for no $M$ is it the case that $ABC \leq MA^B$ for large enough $A,B,C$; for any "large enough" $A,B$, this would imply that $C = O(1)$ is bounded, but $C$ need not be bounded.