General Synonyms:
* Excluded
* Discharged
* Relieved
* Released
* Absolved
* Free
* Not subject to
* Not liable
Specific Synonyms:
* Waived (from a responsibility)
* Exonerated (from a legal obligation)
* Immunized (from a disease)
* Spared (from harm)
* Dispensed with (a requirement)
Formal Synonyms:
* Exonerated
* Dispensed
* Relieved
* Absolved
* Discharged
Informal Synonyms:
* Let off the hook
* Given a pass
* Got out of
* Not required to
The best synonym for "exempted" will depend on the specific context and the nuance you want to convey.