Replace pattern for exponentials

Question

Ultimately, I want to replace every Exp[(const) w[i,j]] to T[i,j] and Exp[-(const) w[i,j]] to 1/T[i,j] in the following expression

(-1 + (E^(w[1, 0] - 1.55432 w[1, 1]) - 
E^(-w[1, 0] + 1.55432 w[1, 1]))^2/(E^(w[1, 0] - 1.55432 w[1, 1]) +
 E^(-w[1, 0] + 1.55432 w[1, 1]))^2)

However, when I use the replacement rule

/. (E^(x[i_, j_] w[i_, j_] + x[m_, l_] w[m_, l_]))-> (E^(x[i, j] w[i, j]) E^(x[m, l] w[m, l]))

as an intermediate step, the replacement does not do anything on the expression. Any suggestion?

Thanks, SJS

Answer 1

expr = (-1 + (E^(w[1, 0] - 1.55432 w[1, 1]) - E^(-w[1, 0] + 1.55432 w[1, 1]))^2 /
             (E^(w[1, 0] -  1.55432 w[1, 1]) + E^(-w[1, 0] + 1.55432 w[1, 1]))^2)

expr /. Power[E, Plus[x_, y__]] :> Inactive[Times][Power[E, x], Power[E, y]]/. 
    {Power[E, Times[c_, w[i_, j_], ___]] :> Power[T[i, j], Sign[c]],
     Power[E,  w[i_, j_]] :>T[i, j]} //Activate

For version 9:

expr /. Power[E, Plus[x_, y__]] :> times[Power[E, x], Power[E, y]] /. 
      {Power[E,   Times[c_, w[i_, j_], ___]] :> Power[T[i, j], Sign[c]], 
       Power[E, w[i_, j_]] :> T[i, j]} /. times -> Times

Update: A slightly more general form allows arbitrary number of terms in the exponent:

f = # /. Power -> power /.  power[E, x : PatternSequence[___]] :> ( 
     Times @@ (power[E, #] & /@ x)) /. 
     {power[E, Times[c_, w[i_, j_], ___]] :> Power[T[i, j], Sign[c]], 
      power[E, w[i_, j_]] :> T[i, j]} /. power -> Power &
f @ expr

same output as above

 expr2 = (-1 + (E^(w[1, 0] - 1.55432 w[1, 1] + 2 w[1, 2]) - 
   E^(-w[1, 0] + 1.55432 w[1, 1] - 3 w[3, 1]))^2/
    (E^(w[1, 0] - 1.55432 w[1, 1]) + E^(-w[1, 0] + 1.55432 w[1, 1]))^2)

f @ expr2