  A static spherically symmetric solution is obtained and examined in the
framework of Einstein-power-Yang-Mills-dilaton theory. To derive this exact
solution a dilaton potential $V(\Phi)$ is taken into account. Thermodynamics of
the black hole is also studied, namely we have obtained and investigated the
temperature and heat capacity of the black hole which has allowed us
characterize the stability of the black hole. Using the framework of the
extended thermodynamic phase space we have derived the equation of state for
the black hole. We have studied the Gibbs free energy of the black hole, which
has the behaviour similar for other black holes with dilaton fields. To
characterize the thermal behaviour of the black hole near the critical point we
have written the Ehrenfest's equations and calculated Prigogine-Defay ratio.
