This is the 18370th most frequent Russian word.
эксклюзивностью
"Exclusivity."
The word «эксклюзивностью» is used in the instrumental case here, describing a quality or characteristic of the club, emphasizing its unique and exclusive nature.
Этот клуб славится своей эксклюзивностью.
This club is famous for its exclusiveness.
The term «эксклюзивностью» in this sentence is used in the instrumental case to define the unique characteristic of the collection being admired.
Мы восхищаемся эксклюзивностью её коллекции.
We admire the exclusiveness of her collection.
Here, «эксклюзивностью» indicates the quality being emphasized about the designer's creations.