  Our paper deals with three-dimensional nonsteady Navier-Stokes equations for
non-Newtonian compressible fluids. It contains a~derivation of the relative
energy inequality for the weak solutions to these equations. We show that the
standard energy inequality implies the relative energy inequality.
Consequently, the relative energy inequality allows us to achieve a weak-strong
uniqueness result. In other words, we present that the weak solution of the
Navier-Stokes system coincides with the strong solution emanated from the same
initial conditions as long as the weak solution exists.
