Answer by Edmund for Applying several functions to the same argument

You can use Composition.

Longhand

Composition[#, Exponent[#, Variables[expr]] &] & /@ {f1, f2}

Shorthand

#@*(Exponent[#, Variables[expr]] &) & /@ {f1, f2}

Both give

{f1@*(Exponent[#1, Variables[expr]] &),  f2@*(Exponent[#1, Variables[expr]] &)}

Hope this helps.