This is the 18352nd most frequent Russian word.
экзамену
"Экзамену" is the dative singular form of "экзамен," meaning "exam" or "test" in English.
In this sentence, "экзамену" is the dative case of "экзамен" (exam), used because the verb "готовятся" (prepare) requires its subject to "готовиться к" (to prepare for something) with the noun completed in the dative case.
Студенты готовятся к экзамену по математике.
The students are preparing for the math exam.
In this sentence, "экзамену" occurs in an instructional or situational dative as it relates to timing or conditions preceding the main event stated.
Перед экзамену мы все очень волновались.
Before the exam, we were all very nervous.
Here, "экзамену" is in the dative case again due to the preposition "к" (to, for), which indicates direction, context, or purpose when used before a noun.