  We introduce a $(5+m)$-dimensional vacuum description of five-dimensional
bulk inflaton models with exponential potentials that makes analysis of
cosmological perturbations simple and transparent. We show that various
solutions, including the power-law inflation model recently discovered by
Koyama and Takahashi, are generated from known $(5+m)$-dimensional vacuum
solutions of pure gravity. We derive master equations for all types of
perturbations, and each of them becomes a second order differential equation
for one master variable supplemented by simple boundary conditions on the
brane. One exception is the case for massive modes of scalar perturbations. In
this case, there are two independent degrees of freedom, and in general it is
difficult to disentangle them into two separate sectors.
