Applying replacement rules to products doesn’t work as expected

I have the following issue: I’d like to apply some replacement rules, for example

rules:={f(x)/t :> ff(x), g(x)/t :> gg(x)}

to an expression, e.g. like this:

(f(x)*g(x)/(t^2))/. rules

Surprisingly, this doesn’t give the expected result

ff(x)*gg(x)

How do I fix this? Sorry if it’s an easy question, I’m still a beginner with Mathematica.