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冪乗

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注釈 ^ 単に「指数」と呼ぶ場合、"exponent" に限らず、（数学に限っても）種々の index を意味する場合も多く、文脈に注意を要する（たとえば部分群の指数）。また、（必ずしも冪指数のことでない）"exponent" の訳として冪数が用いられることもある（たとえば群の冪数）。
^ このような実函数の複素解析的延長は一意に定まる。
^ 乗算回数は、 a 32 = {\displaystyle a^{32}=} ( ( ( ( a 2 ) 2 ) 2 ) 2 ) 2 {\displaystyle ((((a^{2})^{2})^{2})^{2})^{2}} を計算するのに 5 回、 a 1 × a 2 × a 8 × a 32 {\displaystyle a^{1}\times a^{2}\times a^{8}\times a^{32}} に 3 回の、合計 8 回かかる。
^ この場合の乗算回数も、下位桁から計算するのと同じく合計 8 回かかる。

出典 ^ a b c 鈴木 2013, p. 319, (PDF p. 5).
^ a b O'Connor, John J.; Robertson, Edmund F., “Etymology of some common mathematical terms”, MacTutor History of Mathematics archive, University of St Andrews, https://mathshistory.st-andrews.ac.uk/Miscellaneous/Mathematical_notation/ .
^ O'Connor, John J.; Robertson, Edmund F., “Abu'l Hasan ibn Ali al Qalasadi”, MacTutor History of Mathematics archive, University of St Andrews, https://mathshistory.st-andrews.ac.uk/Biographies/Al-Qalasadi/ .
^ Cajori, Florian (2007). A History of Mathematical Notations, Vol I. Cosimo Classics. Pg 344. ISBN 1602066841
^ Rene Descartes, Discourse de la Methode ... (Leiden, (Netherlands): Jan Maire, 1637), appended book: La Geometrie, book one, ⇒page 299. From page 299: " ... Et aa, ou a2, pour multiplier a par soy mesme; Et a3, pour le multiplier encore une fois par a, & ainsi a l'infini ; ... " ( ... and aa, or a2, in order to multiply a by itself; and a3, in order to multiply it once more by a, and thus to infinity ; ... )
^ Quinion, Michael. “ ⇒Zenzizenzizenzic - the eighth power of a number”. World Wide Words. 2010年3月19日閲覧。
^ This definition of "involution" appears in the OED second edition, 1989, and Merriam-Webster online dictionary ⇒[1]. The most recent usage in this sense cited by the OED is from 1806.
^ 小学館デジタル大辞泉「冪指数」[2]
^ a b 鈴木 2013, p. 372, (PDF p. 58).
^ See:

⇒Earliest Known Uses of Some of the Words of Mathematics

Michael Stifel, Arithmetica integra (Nuremberg ("Norimberga"), (Germany): Johannes Petreius, 1544), Liber III (Book 3), Caput III (Chapter 3): De Algorithmo numerorum Cossicorum. (On algorithms of algebra.), page 236. Stifel was trying to conveniently represent the terms of geometric progressions. He devised a cumbersome notation for doing that. On page 236, he presented the notation for the first eight terms of a geometric progression (using 1 as a base) and then he wrote: "Quemadmodum autem hic vides, quemlibet terminum progressionis cossica, suum habere exponentem in suo ordine (ut 1ze habet 1. 1? habet 2 &c.) sic quilibet numerus cossicus, servat exponentem sua denominationis implicite, qui ei serviat & utilis sit, potissimus in multiplicatione & divisione, ut paulo inferius dicam." (However, you see how each term of the progression has its exponent in its order (as 1ze has a 1, 1? has a 2, etc.), so each number is implicitly subject to the exponent of its denomination, which [in turn] is subject to it and is useful mainly in multiplication and division, as I will mention just below.) [Note: Most of Stifel's cumbersome symbols were taken from Christoff Rudolff, who in turn took them from Leonardo Fibonacci's Liber Abaci (1202), where they served as shorthand symbols for the Latin words res/radix (x), census/zensus (x2), and cubus (x3).]

^ 鈴木 2013, p. 337, (PDF p. 23).
^ 鈴木 2013, p. 348, (PDF p. 34).
^ 鈴木 2013, p. 350, (PDF p. 36).
^ 王青翔『「算木」を超えた男』東洋書店、東京、1999年。.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}ISBN 4-88595-226-3。

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