Evaluating each option to identify the correct spelling:
1. exaggerate: Correct. This term denotes presenting something as larger, superior, or inferior to its actual state.
2. exegerate: Incorrect. The spelling is flawed by the omission of the second "g" and the use of "e" instead of "a".
3. exaggarate: Incorrect. This spelling erroneously includes an additional "a" and an unnecessary double "g".
4. exeggarate: Incorrect. This spelling incorrectly combines a misspelling of the "egg" segment with an extra "e".
Consequently, "exaggerate" is the sole correct spelling.