This is the 12688th most frequent Russian word.
корпорацией
The Russian word "корпорацией" means "corporation" in English.
The word "корпорацией" is used in the instrumental case because it indicates the entity being managed.
Она управляет крупной корпорацией.
She manages a large corporation.
Here, "корпорацией" is in the instrumental case to denote the means of collaboration.
Города тесно сотрудничают с корпорацией.
The cities closely collaborate with the corporation.
In this sentence, "корпорацией" is again in the instrumental case to express the entity with which there is an association.