Tachyonic scalar field-driven late universe with dust matter content is considered. The cosmic expansion is modeled with power-law and phantom power-law expansion at late time, i.e. z≲0.45. WMAP7 and its combined data are used to constraint the model. The forms of potential and the field solution are different for quintessence and tachyonic cases. Power-law cosmology model (driven by either quintessence or tachyonic field) predicts unmatched equation of state parameter to the observational value, hence the power-law model is excluded for both quintessence and tachyonic field. In the opposite, the phantom power-law model predicts agreeing valued of equation of state parameter with the observational data for both quintessence and tachyonic cases, i.e. \documentclass[12pt]{minimal}
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\begin{document}$w_{\phi, 0} = -1.49^{+11.64}_{-4.08}$\end{document} (WMAP7+BAO+H0) and \documentclass[12pt]{minimal}
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\begin{document}$w_{\phi, 0} = -1.51^{+3.89}_{-6.72} $\end{document} (WMAP7). The phantom-power law exponent β must be less than about −6, so that the −2<wϕ,0<−1. The phantom power-law tachyonic potential is reconstructed. We found that dimensionless potential slope variable Γ at present is about 1.5. The tachyonic potential reduced to V=V0ϕ−2 in the limit Ωm,0→0.
