  We study higher dimensional quartic quasi-topological black holes in the
framework of non-abelian power-Yang-Mills theory. It is shown that real
solutions of the gravitational field equations exist only for positive values
of quartic quasi-topological coefficient. Depending on the values of the mass
parameter and Yang-Mills charge, they can be interpreted as black holes with
one horizon, two horizons and naked singularity. It is also shown that the
solution associated with these black holes has an essential curvature
singularity at the centre $r=0$. Thermodynamic and conserved quantities for
these black holes are computed and we show that the first law has been
verified. We also check thermodynamic stability in both canonical and grand
canonical ensembles. In addition to this, we also formulate new
power-Yang-Mills black hole solutions in pure quasi-topological gravity. The
physical and thermodynamic properties of these black holes are discussed as
well. It is concluded that unlike Yang-Mills black holes there exist stability
regions for smaller power-Yang-Mills black holes in grand canonical ensemble.
Finally, we discuss the thermodynamics of horizon flat power-Yang-Mills
rotating black branes and analyze their thermodynamic and conserved quantities
by using the counter-term method inspired by AdS/CFT correspondence.
