  We consider the gravity interacting with matter scalar fields and quantized
in the minisuperspace approach in which the wave functional is described by the
Wheeler-DeWitt equations (WdW). Assuming the domination of the homogeneous and
isotropic geometry the leading contributions to the wave functional in the
approximation of the minisuperspace with Friedmann-Robertson-Walker metric
(FRW) and spatially uniform scalar fields are considered. The model of several
scalar fields with exponential potentials and kinetic terms admitting such a
special mixing that ultimately it is possible to separate the variables in the
WdW equation and to find its exact solution in terms of the special functions
is proposed. The semiclassical approximation is thoroughly investigated and the
boundary conditions permitting the physical solution selection for classical
cosmologies are chosen.
