Final answer:
1) Autoclaving. Autoclaving is the recommended method for sterilizing the high-speed handpiece as it relies on moist-heat sterilization.
Step-by-step explanation:
The recommended method for sterilizing the high-speed handpiece is autoclaving. Autoclaves rely on moist-heat sterilization to raise temperatures above the boiling point of water and sterilize items without damaging them. Autoclaving is considered the most effective method of sterilization and is commonly used in medical settings.