We report the precise resistivity data in the ferromagnetic state of high-quality epitaxial thin films of La_1-xCa_xMnO₃. The data below 100 K can be perfectly fit by ρ = ρ_o + BT^4.5 + C/sinh ²(ℏω_s/2k_BT). Here ρ_o is the residual resistivity, the second term arises from two-magnon scattering, and the third term is associated with small-polaron coherent motion which involves a relaxation due to a soft optical phonon mode. Such a soft mode is related to the tilt/rotation of the oxygen octahedra, and has a low frequency (ℏω_s/k_B ~ 80 K). The present result provides an important constraint on the fundamental physics of manganites.