IPA: /ˌɪnɪɡˈzɔːstəblɪ/
KK: /ɪnɪgˈzɔstəblɪ/
In a way that cannot be exhausted or used up; endlessly or without limit.
She worked inexhaustibly on her project, never seeming to tire.
Inexhaustibly → It is formed from "in-" (meaning not), "exhaustus" (from Latin "exhaurire", meaning to draw out or drain), and "-ible" (meaning capable of). The word means not capable of being drained or exhausted, indicating an endless supply or resource.
Think of 'not' ('in-') being able to 'drain' ('exhaustus') something completely — that's why inexhaustibly means something that cannot be exhausted.