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transforming exponential of sums into product of exponentials


Dear All,

I can not understand why Mathmatica refuses to apply rules which transform
exponenials of sums into product of exponentails.

For instance,
f[x+y] /. f[a_ + b_]-> f[a] f[b] returns f[x] f[y],
whereas
Exp[x+y] /. Exp[a_+b_]->Exp[a]Exp[b] still returns Exp[x+y]

Any help greatly appreciated






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