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 law 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 .