  Late-time power law expansion has been proposed as an alternative to the
standard cosmological model and shown to be consistent with some low-redshift
data. We test power law expansion against the standard flat $\Lambda$CDM
cosmology using goodness-of-fit and model comparison criteria. We consider Type
Ia supernova (SN Ia) data from two current compilations (JLA and Union2.1)
along with a current set of baryon acoustic oscillation (BAO) measurements that
includes the high-redshift Lyman-$\alpha$ forest measurements from BOSS
quasars. We find that neither power law expansion nor $\Lambda$CDM is strongly
preferred over the other when the SN Ia and BAO data are analyzed separately
but that power law expansion is strongly disfavored by the combination. We
treat the $R_\text{h} = ct$ cosmology (a constant rate of expansion) separately
and find that it is conclusively disfavored by all combinations of data that
include SN Ia observations and a poor overall fit when systematic errors in the
SN Ia measurements are ignored, despite a recent claim to the contrary. We
discuss this claim and some concerns regarding hidden model dependence in the
SN Ia data.
