  We discuss the 21cm power spectrum (PS) following the completion of
reionization. In contrast to the reionization era, this PS is proportional to
the PS of mass density fluctuations, with only a small modulation due to
fluctuations in the ionization field on scales larger than the mean-free-path
of ionizing photons. We derive the form of this modulation, and demonstrate
that its effect on the 21cm PS will be smaller than 1% for physically plausible
models of damped Ly-alpha systems. In contrast to the 21cm PS observed prior to
reionization, in which HII regions dominate the ionization structure, the
simplicity of the 21cm PS after reionization will enhance its utility as a
cosmological probe by removing the need to separate the PS into physical and
astrophysical components. As a demonstration, we consider the Alcock-Paczynski
test and show that the next generation of low-frequency arrays could measure
the angular distortion of the PS at the percent level for z~3-5.
