The uplink of interference-limited cellular networks with base stations that have large numbers of antennas and use linear Minimum-Mean-Square Error (MMSE) processing with power control is analyzed. Simple approximations, which are exact in an asymptotic sense, are provided for the spectral efficiencies (b/s/Hz) of links in these systems. It is also found that when the number of base-station antennas is moderately large, and the number of mobiles in the entire network is large, correlations between the transmit powers of mobiles within a given cell do not significantly influence the spectral efficiency of the system. As a result, mobiles can perform simple power control (e.g. fractional power control) that does not depend on other users in the network, reducing system complexity and improving the analytical tractability of such systems.