  In this paper, power-law cosmology whose scale factor is a power of time, $a
\propto t^{\a}$, is investigated. Considering late universe with canonical
scalar field and dust domination, we use observational data from Cosmic
Microwave Background (WMAP7), Baryon Acoustic Oscillations (BAO) and
observational Hubble data to find power exponent $\a$ of the power-law and
other cosmological variables. The power $\a$ is found to be $0.99 \pm 0.02$
(WMAP7+BAO+$H_0$) and $0.99 \pm 0.04$ (WMAP7). These values do not exclude
possibility of acceleration at 1$\sigma$ hence giving viability to power-law
cosmology in general. When considering scenario of canonical scalar field dark
energy with power-law expansion, we derive scalar field potential, exact
solution, equation of state parameter and plots their evolutions using
observational data. We confirm that the scenario of power-law cosmology
containing dynamical canonical scalar field is ruled out by WMAP7 data since
its present value of equation of state parameter does not match the WMAP7
result, i.e. the scalar-field power-law cosmology using WMAP7 gives $w_{\phi,
0} = -0.4493 \pm 0.0300 $ while the $w_{\phi}$CDM with WMAP7 data allows a
maximum (+1$\sigma$) value of the equation of state parameter at $w_{\phi, 0} =
-0.69$.
