  In this paper, we extend the study on the nonlinear power-law Maxwell field
to dilaton gravity. We introduce the $(n+1)$-dimensional action in which
gravity is coupled to a dilaton and power-law nonlinear Maxwell field, and
obtain the field equations by varying the action. We construct a new class of
higher dimensional topological black hole solutions of Einstein-dilaton theory
coupled to a power-law nonlinear Maxwell field and investigate the effects of
the nonlinearity of the Maxwell source as well as the dilaton field on the
properties of the spacetime. Interestingly enough, we find that the solutions
exist provided one assumes three Liouville-type potentials for the dilaton
field, and in case of the Maxwell field one of the Liouville potential
vanishes. After studying the physical properties of the solutions, we compute
the mass, charge, electric potential and temperature of the topological dilaton
black holes. We also study thermodynamics and thermal stability of the
solutions and disclose the effects of the dilaton field and the power-law
Maxwell field on the thermodynamics of these black holes. Finally, we comment
on the dynamical stability of the obtained solutions in four-dimensions.
