Exam day or exam's day? [closed]

Although the sentence might be phrased as "I will see you on the day of the exam," that doesn't mean that it can be rearranged with the so-called "Saxon genitive," "exam's day". In "day of x", x describes what happens on the day: day of the exam, Day of Judgement, and so on. The day doesn't belong to the exam, or judgement.

So when moving the describing noun to before the main noun (moving exam to before day), exam is a noun used as an adjective to describe the day (an "attributive noun"). Such nouns are not inflected for case or gender because adjectives are not inflected. Thus it should be left alone and "on the exam day" is right.

That said, "the day of the exam" is probably more idiomatic.