  The principle of dynamic equivalence between soft-sphere and hard-sphere
fluids [Phys. Rev. E \textbf{68}, 011405 (2003)] is employed to describe the
interplay of the effects of varying the density n, the temperature T, and the
softness (characterized by a softness parameter {\nu}^{-1}) on the dynamics of
glass-forming soft-sphere liquids in terms of simple scaling rules. The main
prediction is that the dynamic parameters of these systems, such as the
{\alpha}-relaxation time and the long-time self-diffusion coefficient, depend
on n, T, and {\nu} only through the reduced density n^\ast \equiv
n{\sigma}^{3}_{HS}(T, {\nu}),where the effective hard-sphere diameter
{\sigma}_{HS}(T, {\nu}) is determined, for example, by the
Andersen-Weeks-Chandler condition for soft-sphere-hard-sphere structural
equivalence. A number of scaling properties observed in recent simulations
involving glass-forming fluids with repulsive short range interactions are
found to be a direct manifestation of this general dynamic equivalence
principle. The self-consistent generalized Langevin equation (SCGLE) theory of
colloid dynamics is shown to accurately capture these scaling rules
