  For zero energy, $E=0$, we derive exact, classical and quantum solutions for
{\em all} power-law oscillators with potentials $V(r)=-\gamma/r^\nu$,
$\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero,
these solutions lead to the classical orbits $\r(t)= [\cos \mu
(\th(t)-\th_0(t))]^{1/\mu}$, with $\mu=\nu/2-1 \ne 0$. For $\nu>2$, the orbits
are bound and go through the origin. We calculate the periods and precessions
of these bound orbits, and graph a number of specific examples. The unbound
orbits are also discussed in detail. Quantum mechanically, this system is also
exactly solvable. We find that when $\nu>2$ the solutions are normalizable
(bound), as in the classical case. Further, there are normalizable discrete,
yet {\it unbound}, states. They correspond to unbound classical particles which
reach infinity in a finite time. Finally, the number of space dimensions of the
system can determine whether or not an $E=0$ state is bound. These and other
interesting comparisons to the classical system will be discussed.
