“You don’t exchange something `with’ something. You usually exchange something `for’ something.
Examples: “Saritha exchanged her old VCR for a new one.” “My father is planning to exchange his old scooter for a new one”. ” The old farmer exchanged his wheat for oil.”
You `exchange something for something’ and you `exchange something with someone’.” “In other words, you use `exchange with’ to indicate trading between people, not between things.”
Examples: “The two students exchanged coats with each other.” “Sujatha exchanges books with many of her friends.” “I exchange greetings with Ajit on 1st January. That’s the only time I ring him up.”