The power law of sensory adaptation was introduced more than 50 years ago. It is characterized by action potential adaptation that follows fractional powers of time or frequency, rather than exponential decays and corresponding frequency responses. Power law adaptation describes the responses of a range of vertebrate and invertebrate sensory receptors to deterministic stimuli, such as steps or sinusoids, and to random (white noise) stimulation. Hypotheses about the physical basis of power law adaptation have existed since its discovery. Its cause remains enigmatic, but the site of power law adaptation has been located in the conversion of receptor potentials into action potentials in some preparations. Here, we used pseudorandom noise stimulation and direct spectral estimation to show that simulations containing only two voltage activated currents can reproduce the power law adaptation in two types of spider mechanoreceptors. Identical simulations were previously used to explain the different responses of these two types of sensory neurons to step inputs. We conclude that power law adaptation results during action potential encoding by nonlinear combination of a small number of activation and inactivation processes with different exponential time constants.