We consider a multiplicative multiple access channel in the presence of additive white Gaussian noise. Under individual average power constraints at each of the transmitters, we characterize the capacity region of this channel. The structure of the region reveals some fundamental characteristics related to timesharing, power constraints and the auxiliary random variables present in the converse theorems. As an example, it is shown that to achieve the capacity region of a two user multiplicative MAC, time-sharing of 3 strategies/rate-pairs are required, as opposed to the sufficiency of time-sharing between at most 2 rate-pairs in a discrete memoryless MAC.