Suppose I have quantum gates (i.e. unitary matrices) $A$ and $B$, and I want to implement $(AB)^x$ in a circuit. If $x$ is integer, I can simply apply $A B$ repeatedly $x$-times. But what if $x$ is a real number? Is there a way to decompose $(A B)^x$ into say a product of powers of $A$ and $B$? I'm fine with some approximation.

I was thinking there might be a relation to Hamiltonian Simulation and I also looked into Trotter formulas, but could not see how to do it. In general $A$ and $B$ do not commute.