c. 1300, pouer, "ability; ability to act or do; strength, vigor, might," especially in battle; "efficacy; control, mastery, lordship, dominion, ability or right to command or control; legal power or authority; authorization; military force, an army," from Anglo-French pouair, Old French povoir, noun use of the infinitive, "to be able," earlier podir (9c.), from Vulgar Latin *potere (source also of Spanish poder, Italian potere), from Latin potis "powerful" (from PIE root *poti- "powerful; lord").
Whatever some hypocritical ministers of government may say about it, power is the greatest of all pleasures. It seems to me that only love can beat it, and love is a happy illness that can't be picked up as easily as a Ministry. [Stendhal "de l'Amour," 1822]
Meaning "one who has power, person in authority or exercising great influence in a community" is late 14c. Meaning "a specific ability or capacity" is from early 15c. In mechanics, "that with which work can be done," by 1727.
Sense of "property of an inanimate thing or agency of modifying other things" is by 1590s. Meaning "a state or nation with regard to international authority or influence" [OED] is from 1726. Meaning "energy available for work is from 1727. Sense of "electrical supply" is from 1896.
Colloquial a power of for "a large quantity of, a great number of" is from 1660s (compare powerful). Phrase the powers that be "the authorities concerned" is from Romans xiii.1. As a statement wishing good luck, more power to(someone) is recorded from 1842. A man-advantage power play in ice hockey so called by 1940. Power failure "failure of the (electrical) power supply" is from 1911; power steering in a motor vehicle is from 1921. Power politics "political action based on or backed by threats of force" (1937) translates German Macht-politik.
c. 1100, "celebration of public worship," from Old French servise "act of homage; servitude; service at table; Mass, church ceremony," from Latin servitium "slavery, condition of a slave, servitude," also "slaves collectively," from servus "slave" (see serve (v.)).
Meaning "act of serving, occupation of an attendant servant" is attested from c. 1200, as is that of "assistance, help; a helpful act." From c. 1300 as "provision of food; sequence of dishes served in a meal;" from late 14c. as "service at table, attendance during a meal." Meaning "the furniture of the table" (tea service, etc.) is from mid-15c.
Meanings "state of being bound to undertake tasks for someone or at someone's direction; labor performed or undertaken for another" are mid-13c. Sense of "service or employment in a court or administration" is from c. 1300, as is that of "military service (especially by a knight); employment as a soldier;" hence "the military as an occupation" (1706).
Also in Middle English "sexual intercourse, conjugal relations" (mid-15c.; service of Venus, or flesh's service). Service industry (as distinct from production) attested from 1938. A service station originally was a gas stop that also repaired cars.
"the executive branch of the public service," as distinguished from the military, naval, legislative, or judicial, 1765, originally in reference to non-military staff of the East India Company, from civil in the sense "not military." Civil servant is from 1792.