Final answer:
Meritocratic or performance-based power best illustrates the concept of power being tied to performance-reward contingencies, which incentivize hard work by offering higher prestige and rewards for more significant contributions.
Step-by-step explanation:
The type of power that best illustrates the idea that power is based on performance-reward contingencies is often referred to as meritocratic power or performance-based power. This concept aligns with the sociological theory proposed by Davis and Moore, which posits that societies reward more important work with higher levels of income, prestige, and power as an incentive for individuals to work harder and achieve more. An example provided describes a situation where students are motivated to work especially hard on a project when they know their performance will be publicly demonstrated, implying public recognition or lack thereof as a form of power influence.