The current work aimed to understand how the Reynolds number affected the characteristics of turbulent power-law fluids. A fully developed large-eddy simulation of turbulent pseudoplastic and dilatant fluids over a straight pipe was performed numerically at three Reynolds numbers (4,000; 8,000 and 12,000) and flow behaviour indexes of (0.75, 1 and 1.4). The key findings indicated that when the Reynolds number rose, the creation of axial fluctuations close to the wall area was amplified significantly. This led to a notably improved kinetic energy of turbulent fluctuations across the radial direction. The mechanism of the velocity variations from the near-wall area towards the core region was enhanced with rising Reynolds numbers. This trend was more evident as the flow behaviour index dropped.