In this paper , we show that the expansion history of the Universe in power-law cosmology essentially depends on two crucial parameters , namely the Hubble constant H _ { 0 } and deceleration parameter q .
We find the constraints on these parameters from the latest H ( z ) and SNe Ia data .
At 1 \sigma level the constraints from H ( z ) data are obtained as q = -0.18 _ { -0.12 } ^ { +0.12 } and H _ { 0 } = 68.43 _ { -2.80 } ^ { +2.84 } km s ^ { -1 } Mpc ^ { -1 } while the constraints from the SNe Ia data read as q = -0.38 _ { -0.05 } ^ { +0.05 } and H _ { 0 } = 69.18 _ { -0.54 } ^ { +0.55 } km s ^ { -1 } Mpc ^ { -1 } .
We also perform the joint test using H ( z ) and SNe Ia data , which yields the constraints q = -0.34 _ { -0.05 } ^ { +0.05 } and H _ { 0 } = 68.93 _ { -0.52 } ^ { +0.53 } km s ^ { -1 } Mpc ^ { -1 } .
The estimates of H _ { 0 } are found to be in close agreement with some recent probes carried out in the literature .
The analysis reveals that the observational data successfully describe the cosmic acceleration within the framework of power-law cosmology .
We find that the power-law cosmology accommodates well the H ( z ) and SNe Ia data .
We also test the power-law cosmology using the primordial nucleosynthesis , which yields the constraints q \gtrsim 0.72 and H _ { 0 } \lesssim 41.49 km s ^ { -1 } Mpc ^ { -1 } .
These constraints are found to be inconsistent with the ones derived from the H ( z ) and SNe Ia data .
We carry out the statefinder analysis , and find that the power-law cosmological models approach the standard \Lambda CDM model as q \rightarrow - 1 .
Finally , we conclude that despite having several good features power-law cosmology is not a complete package for the cosmological purposes .