We considered cosmological model within the framework of the generalized F(R,T) gravity in flat FLRW metric. Earlier, an exponential solution was shown for the generalized case, which describes the inflationary stage of the evolution of the Universe. In this paper, it is shown that for the particular case of the Starobinsky model, the generalized model has, among other things, a power-law solution that describes the dust-like stage and the stage of radiation dominance. It should be noted that this solution was obtained by the analytical method as a solution to the Euler-Lagrange equation for this model, taking into account the functions u, v -describing the relationship between the curvature scalar and the torsion scalar, and depending not only on the first, but also on the second time derivative of the scale factor. This solution is of interest, since it shows not only that this model has a solution, but also that this solution can describe the modern observable Universe for more complex forms u, v than described earlier. This solution allows other related cosmological parameters to be obtained accordingly. The paper presents the parameter for the equation of state, which describes the stage of the evolution of the Universe.