or use a construction something like

F[x] = Feven[x] * Boole[(-1)^n == 1] + Fodd[x] * Boole[(-1)^n == -1]

Thanks, Frank, Blinder and Todd.

I did:

Fcos[x_, n_] := 
             If[n == 1, Cos[x]^n, 
                If[EvenQ[n], Expand[((1 + Cos[2*x])/2)^(n/2)], 
                   Cos[x]*Expand[((1 + Cos[2*x])/2)^((n - 1)/2)]]]

z = Factor[Expand[Cos[A]^9 //. {Cos[x_]^k_ -> Fcos[x, k]}]]

giving

1/128 Cos[A] (35 + 48 Cos[2 A] + 28 Cos[4 A] + 16 Cos[2 A] Cos[4 A] + Cos[8 A])

If you go back from this expression with Simplify[] you get again Cos[A]^9

Thanks again. Today is my 2nd day with Mathematica.

César Lozada