  We find exact cosmological solutions when the Newton parameter and the
cosmological term are dynamically evolving in a renormalization-group improved
Hamiltonian approach. In our derivation we use the Noether symmetry approach,
leading to an interesting variable transformation which yields exact and
general integration of the cosmological equations. The functional dependence of
Lambda on G is determined by the method itself, therefore generalizing previous
results on symmetry principles in cosmology. We find new functional relations
between Lambda and G, jointly with power-law inflation for pure gravity.
