The exact solutions in the standard inflationary model based on the se
lf-interacting scalar field minimally coupled to gravity are considere
d. The shape's freedom of the self-interacting potential V(phi) is pos
tulated to obtain a new set of the exact solutions in the framework of
Friedmann-Robertson-Walker Universes. The general solution was found
in the case of power law inflation. We obtained new solutions and comp
ared them with obtained ones earlier for the exponential type inflatio
n. (C) 1997 Published by Elsevier Science B.V.