I know exchange is 交換 in Japanese but is it right to say "大学交換”?
My current guess of the expression would be
日本に大学交換しに行きます。
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Sign up to join this community交換 is the correct word for "exchange", also in this context.
I think you could say
交換留学で日本に行きます。
I am going to Japan for a student/university exchange.