  Understanding the formation of star clusters with low star-formation
efficiency (SFE) is very important to know about the star-formation history. In
N-body models of star cluster evolution after gas expulsion, the Plummer model
with outer power law density profile has been used massively. We study the
impact of the density profile slopes on the survivability of the low-SFE star
clusters after instantaneous gas expulsion. We compare cases when stellar
cluster has Plummer profile and Dehnen profiles with cusp of different slopes
at the time of formation. We determine the corresponding density profile of the
residual gas for a given global SFE, assuming that our model clusters formed
with a constant efficiency per free-fall time and hence have shallower density
profile of gas than that of stars. We perform direct $N$-body simulations of
evolution of clusters initially in virial equilibrium within gas potential
after gas removal. We find that the violent relaxation lasts no longer than
20~Myr independently of the density profile power law slopes. Dehnen model
clusters survive after violent relaxation with significantly lower SFEs when
the global SFE measured within the Jacobi radius or within a half-mass radius.
Dehnen $\gamma=0$ model clusters show similar final bound fraction with the
Plummer model clusters if global SFE is measured within 10 scale radii. The
final bound fraction increases with $\gamma$ values for a given global SFE. We
conclude that Dehnen clusters better resist the consequences of the violent
relaxation followed the instantaneous gas expulsion than the Plummer clusters.
Thus the shallower the outer density slope of the low-SFE clusters, the better
for their survivability after gas expulsion. Among Dehnen clusters we find that
the steeper the inner slope (cusp) the higher the bound mass fraction is
retained after violent relaxation for a given global SFE.
