Exactly

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late Middle English (as a verb): from Latin exact- ‘completed, ascertained, enforced’, from the verb exigere, from ex- ‘thoroughly’ + agere ‘perform’. The adjective dates from the mid 16th century and reflects the Latin exactus ‘precise’.

wiktionary

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exact +‎  -ly

etymonline

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exactly (adv.)

"in an exact manner, with minute correctness," 1530s, from exact (adj.) + -ly (2). Elliptical use for "quite right" not recorded before 1869.