Final answer:
Charismatic authority is based on leaders' extraordinary personal abilities that inspire devotion in followers.
Step-by-step explanation:
The type of authority belonging to leaders who rest on their extraordinary personal abilities that inspire devotion and admiration in their followers is known as charismatic authority. This authority is unique because it does not derive from formal laws, traditions, or bureaucracies, but from the remarkable qualities and abilities of a leader that enthuse their followers. Charismatic leaders have historically included a diverse group of individuals and have played various roles across societies, being as likely to be viewed as tyrannical as they are to be considered heroic.