Final answer:
Expert power is a base of power that uses knowledge and expertise to persuade others, making it different from coercive, reward, legitimate, and referent powers.
Step-by-step explanation:
The power base that relies on the use of knowledge to persuade is best described as expert power. This type of power stems from the skills and expertise that a person possesses, which in turn allows them to influence others. Expert power is particularly effective in situations where someone has a significant amount of knowledge in a specific area that others do not have, making their advice or opinion highly valued and persuasive.
In contrast, coercive power is based on the ability to punish, reward power is based on the ability to provide benefits, legitimate power comes from a formal position, and referent power comes from personal characteristics that command respect, such as charisma. Out of the options provided, expert power is the most accurate answer since it relies specifically on the use of knowledge and expertise.