word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1530s, "to draw off or out, to use up completely," from Latin exhaustus, past participle of exhaurire "draw off, take away, use up, empty," from ex "off" (see ex-) + haurire "to draw up" (as water), from PIE *heusio- "to scoop." Meaning "make weak or helpless, as by fatigue" is from 1630s. Related: Exhausted; exhausting; exhaustible.
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Harper, D. (n.d.). Etymology of inexhaustible. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inexhaustible