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.