Learn Russian: Музыканты должны репетировать десять раз, перед тем как выступать. - The musicians must rehearse ten times before performing.

When the subject is the same for both actions (the musicians), you use the infinitive after перед тем как. This is like saying 'before performing' in English. If the second action had a different subject, you would need to use a past tense verb instead.

Could I use до того как instead of перед тем как in this sentence?

Yes, they are almost always interchangeable! Перед тем как often implies the action happens immediately before the next one, while до того как is a slightly more general 'before'. Both work perfectly here.

Why does the word раз look like it is in the singular after the number десять?

Numbers five and above require the following noun to be in the genitive plural. The word раз (time) is an exception where its genitive plural form has no extra ending, so it looks exactly the same as the nominative singular.

Why are both репетировать and выступать in the imperfective aspect?

Репетировать is imperfective because repeating an action ten times focuses on the recurring process. Выступать is imperfective because it refers to the general idea or routine of performing, rather than one specific, finished event.