The correct answer is B) Legitimate power and expert power. As a first assistant or chief engineer, your authority comes from your legitimate position within the organizational hierarchy, as well as your expert knowledge and skills in the operation and maintenance of the vessel's engineering systems. Legitimate power comes from the formal authority and responsibilities associated with your role, while expert power stems from your specialized expertise that is recognized and respected by the crew. The other options are incorrect because: A) Coercive power and control-of-information power are not the primary sources of authority for a first assistant or chief engineer. C) Reward power and referent power, while potentially relevant, are not the main foundations of authority in this context. D) Absolute power and control-of-information power do not accurately reflect the nature of the authority held by a first assistant or chief engineer.