Exhale

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late Middle English (in the sense ‘be given off as vapour’): from Old French exhaler, from Latin exhalare, from ex- ‘out’ + halare ‘breathe’.

wiktionary

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From Middle French exhaler, from Latin exhalare, from ex(“out”) + halare(“to breathe”).

etymonline

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exhale (v.)

c. 1400, exale, transitive, originally of liquids, perfumes, the breath of life, etc., from Old French exhaler (14c.) and directly from Latin exhalare "breathe out, evaporate," from ex "out" (see ex-) + halare "breathe." Of living things, "to breathe out," 1580s transitive; by 1837 intransitive. Related: Exhaled; exhaling.