Find an operator in a formula with Cases?

Questions
1

Hi,
I would like to search through a formula to find if it contains a divide operator.

f= (a + b)/(c - d) e

Below the surface this is build as

f // FullForm

Times[Plus[a,b],Power[Plus[c,Times[-1,d]],-1],e]

I wrongly though that searching for a Divide operation I could use Cases looking for a pattern Power[__,-1] but this doesn’t work.
I only succeed when converting f in fullform to a string and then use StringCases.

f = f // FullForm // ToString
StringCases[f, __ ~~ "Power[" ~~ __ ~~ ", -1]" ~~ ___]

This returns the expression so I know it found the Divide operation.
Basically I would like to search for any +,*,-,/ operator in any formula like above.
Is there a way by using the formula itself with Cases?

Thx!

2

Add a level specification so Cases looks ‘deeper’:

Cases[f, Power[x__, -1], \[Infinity]]
3

Thanks Sander,
I knew it was a basic thing and now it all came back :slight_smile: (slight feeling of shame..).
Amazing to see that sometimes jou look at the documentation and just miss the important part. I was seeing strings only and not an expression tree.