  In this paper, we present a new class of higher dimensional exact topological
black hole solutions of the Brans-Dicke theory in the presence of a power-law
Maxwell field as the matter source. For this aim, we introduce a conformal
transformation which transforms the Einstein-dilaton-power-law Maxwell gravity
Lagrangian to the Brans-Dicke-power-law Maxwell theory one. Then, by using this
conformal transformation, we obtain the desired solutions. Next, we study the
properties of the solutions and conditions under which we have black holes.
Interestingly enough, we show that there is a cosmological horizon in the
presence of a negative cosmological constant. Finally, we calculate the
temperature and charge and then by calculating the Euclidean action, we obtain
the mass, the entropy and the electromagnetic potential energy. We find that
the entropy does not respect the area law, and also the conserved and
thermodynamic quantities are invariant under conformal transformation. Using
these thermodynamic and conserved quantities, we show that the first law of
black hole thermodynamics is satisfied on the horizon.
