Since the drag is a*v[sup]b[/sup], it means that F=-a*v[sup]b[/sup], here assume a>0.
assume b>1;
F=m dv/dt;
dv/dt= -a*v[sup]b[/sup]/m;
v[sup]-b[/sup] dv= -(a/m) dt
do integration for both side
(1/(-b+1))v[sup]-b+1[/sup]-(1/(-b+1))v[sub]o[/sub][sup]-b+1[/sup]=-at/m

v[sup]-b+1[/sup]= v[sub]o[/sub][sup]-b+1[/sup]+a*(b-1)*t/m
or
v[sup]b-1[/sup]= 1/ (1/ v[sup]b-1[/sup]+a*(b-1)*t/m);

The denominator will become infinity when t approach to infinity, so v become zero.