\begin{document}$ f(R,G) $\end{document} gravity, where R and G are the Ricci scalar and Gauss-Bonnet invariant, respectively. Our model assumes that \begin{document}$ f(R,G) $\end{document} is an exponential function of G combined with a linear combination of R. We scrutinize the observational limitations under a power law cosmology that relies on two parameters, the Hubble constant (\begin{document}$ H_0 $\end{document}) and the deceleration parameter (q) utilizing the 57-point \begin{document}$ H(z) $\end{document} data, 8-point BAO data, 1701-point Pantheon+ data, joint data of \begin{document}$ H(z) $\end{document} + Pantheon, and joint data of \begin{document}$ H(z) $\end{document} + BAO + Pantheon+. The outcomes for \begin{document}$ H_0 $\end{document} and q are realistic within observational ranges. We also address energy conditions, \begin{document}$ Om(z) $\end{document} analysis, and cosmographical parameters such as jerk, lerk, and snap. Our estimate of \begin{document}$ H_0 $\end{document} is remarkably consistent with various recent Planck Collaboration studies that utilize the ΛCDM model. According to our study, power law cosmology within the context of \begin{document}$ f(R,G) $\end{document} gravity provides the most comprehensive explanation of the important aspects of cosmic evolution."> Modified power law cosmology: theoretical scenarios and observational constraints -
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