  A power law cosmology is defined by the cosmological scale factor evolving as
$t^{\alpha}$. In this work, we put bounds on $\alpha$ by using the joint test
of the SNe Ia data from Supernova Legacy Survey (SNLS) and H(z) data with
curvature constant $ k = 0, \pm 1$. We observe that the combined analysis with
SNLS and H(z) data favours the open power cosmology with $\alpha =
1.31^{+0.06}_{-0.05}. It is also interesting to note that an Einstein - de
Sitter model $(\alpha = 2/3)$ is ruled out at $2\sigma$ level.
