This is the 6240th most frequent Russian word.
уважаемого
"Respected" or "esteemed."
Here, 'уважаемого' is used as an adjective meaning 'respected' to describe the director.
Я поблагодарил уважаемого директора за его труд.
I thanked the respected director for his work.
In this sentence, 'уважаемого' modifies 'профессора,' indicating respect for the professor.
Вы получили письмо от уважаемого профессора?
Did you receive a letter from the respected professor?
'Уважаемого' is attributive here, describing the expert as someone held in high regard.