  One of the most relevant solutions in any cosmological model concerning the
evolution of the universe is the power-law solution. For the scalar-tensor
model of dark energy with kinetic and Gauss Bonnet couplings, it is shown that
we can conserve the power-law solution and at the same time meet the recent
observational bound on the speed of gravitational waves. In the FRW background
the anomalous contribution to the speed of gravitational waves, coming from the
kinetic and Gauss-Bonnet couplings, cancel each other for power-law solutions.
It is shown that by simple restriction on the model parameters we can achieve a
non-time-dependent cancellation of the defect in the velocity of the
gravitational waves. The model can realize the cosmic expansion with
contributions from the kinetic and Gauss-Bonnet couplings of the order of
${\cal O}(1)$ to the dark energy density parameter. The results are valid on
the homogeneous FRW background and the limitations of the approach are
discussed.
