Fractional exponent for formal power series over an arbitrary ring

Question

I know that we can define addition and multiplication (and other things related to the ring of formal power series like formal derivative) for formal power series over a ring but can we talk about fractional exponents? For instance $x^{\frac{3}{2}}$? Solving problems by generating functions lead me ask this question. Actually, I need to know if it's necessary to look at the problems with an analytic view (paying attention to and using things like the radius of convergence) or not. We have to show that fractional exponentiation is well-defined in the context of formal power series in order to use it.