Q:

How to compute an exponent in matlab without getting inf even with vpa or sym? 

i have this exp function in matlab
a1=(exp(-beta0*abs(z-zaks)));
b1=(ohmi*exp(-2*beta0*H)*exp(-beta0*(z+zaks)))
c1=(ohmu*exp(beta0*(z+zaks)))
f1=(ohmu*ohmi*exp(-2*beta0*H)*exp(beta0*abs(z-zaks)))
g1=2*beta0*(1-(ohmu*ohmi*exp(-2*beta0*H)))
h1=(a1+b1+exp(c1)+f1)
j1=exp(h1)
gpm=j1/g1

with
beta0=1.411608078945960e+20 + 8.949434210398852e-26i
betai=[1.411608078945960e+20 + 8.949434210398852e-26i 1.411608078945960e+20 +   1.398349095374821e-26i 1.411608078945960e+20 + 1.398349095374821e-27i 1.411608078945960e+20 + 1.398349095374821e-26i]

ohmi=[9.803212783111246e-92 + 2.674639380309578e-46i 2.428723887707741e-93 + 4.457732300515962e-47i -2.428723887707741e-93 - 4.457732300515962e-47i;1.411608078945960e+20 + 1.398349095374821e-26i]

ohmu=1.004853842833425e-91 + 3.169942969255795e-46i
z=zaks=4950
H=5000

and it return to be inf
even if i had using vpa or sym in it
what should go wrong with this? 

A:

It also depends on whether you used vpa correctly:
>> vpa(1e400)

ans =

Inf

>> vpa('1e400')

ans =

1.0e400

So you always have to prevent matlab from evaluating something large/small before using vpa.  Now, this doesn't solve your problem, since
>> vpa(exp(1.3975e+024 +8.8599e-022*i))

ans =

Inf + Inf*i

>> vpa('exp(1.3975e+024 +8.8599e-022*i)')

ans =

Inf + Inf*i

>> exp(vpa('1.3975e+024 +8.8599e-022*i'))

ans =

RD_INF + RD_INF*i

so regardless of the approach you use, you will get infinity for all intents and purposes. 

Why is that, you might ask?  Consider that
exp(710)

ans =

   Inf

Now, your number is roughly equal to
exp(1397500000000000000000000)

or
10^606926538459794441764864

or
1e606926538459794441764864

Of course I ignored a teeny-tiny imaginary part, but that doesn't change much.  You do realise that it's a very big number, right? 
So, as @BillBokeey has already commented: what do you plan to do with this number?  Your best options are probably doing anything you want on paper first, and reach a result that can be handled by a computer.