dispense (v.)youdaoicibaDictYouDict[dispense 词源字典]
early 14c., from Old French dispenser "give out" (13c.), from Latin dispensare "disburse, administer, distribute (by weight)," frequentative of dispendere "pay out," from dis- "out" (see dis-) + pendere "to pay, weigh" (see pendant).

In Medieval Latin, dispendere was used in the ecclesiastical sense of "grant license to do what is forbidden or omit what is required" (a power of popes, bishops, etc.), and thus acquired a sense of "grant remission from punishment or exemption from law," hence "to do away with" (1570s), "do without" (c. 1600). Older sense is preserved in dispensary. Related: Dispensed; dispensing.[dispense etymology, dispense origin, 英语词源]
licence (n.)youdaoicibaDictYouDict
mid-14c., "liberty (to do something), leave," from Old French licence "freedom, liberty, power, possibility; permission," (12c.), from Latin licentia "freedom, liberty, license," from licentem (nominative licens), present participle of licere "to be allowed, be lawful," from PIE root *leik- "to offer, bargain" (cognates: Lettish likstu "I come to terms"). Meaning "formal (usually written) permission from authority to do something" (marry, hunt, drive, etc.) is first attested early 15c. Meaning "excessive liberty, disregard of propriety" is from mid-15c. There have been attempts to confine license to verbal use and licence to noun use (compare advise/advice, devise/device.
warrant (n.)youdaoicibaDictYouDict
c. 1200, "protector, defender," from Old North French warant "defender; surety, pledge; justifying evidence" (Old French garant), from Frankish *warand, from Proto-Germanic *war- "to warn, guard, protect" (cognates: Old High German werento "guarantor," noun use of present participle of weren "to authorize, warrant;" German gewähren "to grant"), from PIE root *wer- (5) "to cover" (see weir).

Sense evolved via notion of "permission from a superior which protects one from blame or responsibility" (early 14c.) to "document conveying authority" (1510s). A warrant officer in the military is one who holds office by warrant (as from a government department), rather than by commission (from a head of state).
exeatyoudaoicibaDictYouDict
"A permission from a college, boarding school, or other institution for temporary absence", Early 18th century: from Latin, 'let him or her go out', third person singular present subjunctive of exire (see exit).