The well-width dependence of the two-dimensional (21)) electron energy relaxation associated with acoustic-phonon emission in GaAs/Ga1-xAlxAs multiple quantum wells (MQWs) has been investigated using Shubnikov-de Haas (SdH) effect measurements in the temperature range of 3.3-15 K and at applied electric fields up to 300 V m(-1). The modulation-doped MQW samples studied have quantum-well widths (L-z) in the range between 40 and 145 Angstrom; only the lowest subband in each sample is populated with a 2D carrier density in the range from 1.04 x 10(16) m(-2) to 1.38 x 10(16) m(-2). The power loss-electron temperature characteristics of the samples have been obtained from the lattice temperature and electric field dependences of the amplitude of the SdH oscillations. It is found that the power loss, decreases markedly when L-z increases from 40 Angstrom to about 120 Angstrom and it increases for L-z > 120 Angstrom. The experimental results are compared with the current 2D and three-dimensional (3D) theoretical models for power loss, which include both piezoelectric and deformation-potential scattering. The electron-temperature dependence of power loss determined experimentally fits well to both the 2D and 3D theoretical models in the intermediate-temperature regime but with different values for the acoustic deformation potential. It is shown that for samples with L-z in the range of 40-120 Angstrom, the 2D model predicts a dependence of power loss on the well width, which is similar to that observed experimentally. The 3D model, however, predicts a power loss which increases with increasing well width and describes well the well-width dependence of the experimental power loss for wide wells (L-z greater than or equal to 120 Angstrom). The results provide useful information about the relative magnitude of the deformation-potential and piezoelectric contributions to power loss.