Is the power and the legitimacy of a director based on his knowledge and his skills?

Power and legitimacy of the Director is based on his/her skills, knowledge, strategic thinking, connections with the higher ups  as well as in the  community  and his/her overall contribution to the output.  His/her output must also be several times higher than his/her salary otherwise he /she would not survive long in the company.

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If He-She real skilled and has a wide knowledge , so yes power based on it, but if he-she has not their power worth nothing.

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agree with all expert answers

Not that sure thing but based on his rank in between employees "Job Rank of authority" which s based mainly on his- her education and experience.