Neutral-pion pi(0) spectra were measured at midrapidity (vertical bar y vertical bar < 0.35) in Au + Au collisions at root s(NN) = 39 and 62.4 GeV and compared with earlier measurements at 200 GeV in a transverse-momentum range of 1 < p(T) < 10 GeV/c. The high-p(T) tail is well described by a power law in all cases, and the powers decrease significantly with decreasing center-of-mass energy. The change of powers is very similar to that observed in the corresponding spectra for p + p collisions. The nuclear modification factors (RAA) show significant suppression, with a distinct energy, centrality, and p(T) dependence. Above p(T) = 7 GeV/c, R-AA is similar for root sNN = 62.4 and 200 GeV at all centralities. Perturbative-quantum-chromodynamics calculations that describe R-AA well at 200 GeV fail to describe the 39 GeV data, raising the possibility that, for the same p(T) region, the relative importance of initial-state effects and soft processes increases at lower energies. The p(T) range where pi(0) spectra in central Au + Au collisions have the same power as in p + p collisions is approximate to 5 and 7 GeV/c for root sNN = 200 and 62.4 GeV, respectively. For the root sNN = 39 GeV data, it is not clear whether such a region is reached, and the x(T) dependence of the x(T)-scaling power-law exponent is very different from that observed in the root sNN = 62 and 200 GeV data, providing further evidence that initial-state effects and soft processes mask the in-medium suppression of hardscattered partons to higher p(T) as the collision energy decreases.