We find the exact general solution for cosmological models arising fro
m the interaction of the gravitational field with two scalar fields in
both Bat Robertson-Walker and the locally rotationally symmetric Bian
chi I spacetime filled with an exponential potential. One scalar field
self-interacts with this potential and the other is a free massless s
calar field. The solutions have a singularity and a set of these exhib
it the transition to power-law inflation for both metrics.