Power laws are omnipresent and actively studied in many scientific fields, including plasticity of materials. Here, we report the power-law statistics in the second and subsequent pop-in magnitudes during load-controlled nanoindentation testing, whereas the first pop-in is characterized by Gaussian-like statistics with a well-defined average value. The transition from Gaussian-like to power-law is due to the change in the deformation mechanism from dislocation nucleation to dislocation network evolution in the sharp-indenter induced abruptly decaying stress and dislocation density fields. Based on nanoindentation testing on the (100) and (111) surfaces of body-centered cubic (BCC) iron and the (100) surface of face-centered cubic (FCC) copper, the scaling exponents of the power laws were determined to be 5.6, 3.9, and 6.4, respectively. These power-law exponents are much higher than those typically observed in micro-pillar plasticity (1.0-1.8), suggesting that the nanoindentation plasticity belongs to a different universality class than the micro-pillar plasticity. Although power laws are observed during nanoindentation and the power-law exponents are estimated to be approximately 1.5-1.6 for face-centered cubic metals, the origin of the exponent remains unclear. In this paper, we show the power-law statistics in pop-in magnitudes and unveil the nature of the exponent.