I am not good in patterns in Mathematica, and so can’t figure what I am doing wrong.

This example works, when the exponent is 1

ClearAll[y,x,n] Cases[{( y[x]/x)^1}, (y[x]/x )^(n_.) :> n] 

But when exponent is 2 it does not find it

 Cases[{( y[x]/x)^2}, (y[x]/x )^(n_.) :> n] 

Help says

I think this happens, because the font end changes (y[x]/x)^2 to y[x]^2/x^2 before Cases gets hold of it? So the pattern is lost. But when I tried

   Cases[{( y[x]/x)^2}, (y[x]^n_.)/(x^n_.):>n] 

It still returned {}

What is the correct way to handle this? I need to find all powers of expressions of form y[x]/x

Tried HoldForm and Verbatim and Inactive but can’t get it to work.