Is it makeup or make-up or make up?

You said:

You can make-up the makeup exam.

Unless it's a make-up exam about cosmetics, this wouldn't be what you're looking for, especially since "make-up" is a descriptor and "make up" is an action.

You can make up the make-up exam.

Would be a consistent, sensible convention. As noted by @J.R. below, it's not necessarily correct since Harvard lists both. However, this is the convention that I would use.

[Make up] as the action and [make-up] as the descriptor.

Makeup as a compound word used to represent cosmetics.

1. Make up (verb)

   • Make up you mind. (to settle)
   • Twenty kids make up the class. (to constitute)

2. Makeup (noun, or attributive adjective)

   • The makeup of the diverse sample is reflective of the population at risk for diseases.

   • He wore makeup. (cosmetics, sometimes "make-up")

   • We will take a makeup test. (something that makes up for)

If you have to take a test over, you make up the test. The test you make up is a make-up test. Be sure to put on your makeup before making up the make-up test. (When used as an adjective, make-up requires a hyphen.)

As stated previously, "make up" is a verb, "make-up" is an adjective, and "makeup" is a noun. Therefore, if an esthetics student missed an exam on cosmetics and then missed the alternative exam, it is possible that the student would have to make up a make-up makeup exam.