Aperiodic electroencephalography (EEG) activity is hypothesized to index biological mechanisms that underpin brain functioning. This longitudinal study characterized the developmental trajectories of the aperiodic slope (i.e., aperiodic exponent) and offset from infancy to 7 years of age in a US community sample (N = 391, 46.5% female, predominantly White; data collection 2013-2023). The study further examined whether differential developmental trajectories resulted in differential associations between child aperiodic activity and maternal anxiety symptoms. Developmental trajectories for slope and offset were nonlinear and characterized by relative increases in early childhood and a subsequent decrease or stabilization by Age 7, with variation by brain region and sex. Maternal anxiety was negatively associated with slope at 3 years and positively associated with slope at 7 years. Implications for child brain development are discussed.