Talk:Exponentiation

Exponentiation was one of the good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Article milestones
Date	Process	Result
April 7, 2007	Good article nominee	Listed
September 8, 2007	Good article reassessment	Kept
August 5, 2021	Good article reassessment	Delisted

Current status: Delisted good article

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Did you know nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: rejected by Theleekycauldron (talk) 10:57, 25 December 2022 (UTC)[reply]

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... that exponentiation is basically repeated multiplication? Source: https://mathinsight.org/exponentiation_basic_rules
- Reviewed:
- Comment: My first nomination submission.

Created by Slaythe (talk). Self-nominated at 01:05, 24 December 2022 (UTC).[reply]

Sorry, Slaythe, but it's not eligible, because it hasn't been created, 5x expanded, or designated a Good Article within the last week. Please see WP:DYKCRIT. It you get it promoted to Good Article status, you may resubmit a DYK nomination. MANdARAX • XAЯAbИAM 01:34, 24 December 2022 (UTC)[reply]

Proposed merge of Base (exponentiation) into Exponentiation

stub article with limited potential for growth; it could be covered under Exponentiation#Terminology and Exponentiation#Powers via logarithms. fgnievinski (talk) 15:14, 23 January 2025 (UTC)[reply]

I agree to redirect of Exponentiation, but not to a section, as "base" is defined in the first sentence of this article. This is so evident that I'll do this immediately. D.Lazard (talk) 15:52, 23 January 2025 (UTC)basis[reply]

I don't think there's any benefit in making the word "base" bold here. Italic is completely fine for this. –jacobolus (t) 18:29, 23 January 2025 (UTC)[reply]

MOS:BOLDREDIRECT suggests that "base" and "exponent" must be bolded as targets of redirects. D.Lazard (talk) 21:04, 23 January 2025 (UTC)[reply]

"Terms which redirect to an article or section are commonly bolded" is not the same at all as a hypothetical "every term which redirects must be bolded". In my opinion it is worth using bold for (a limited number of) synonyms of the main title, or on words in later sections of an article which could plausibly be their own article. Bolding every glossary-type term related to a topic is overdoing it: distracting but not really helpful to anyone. (MOS even explicitly says: "Avoid using boldface for introducing new terms.") –jacobolus (t) 23:03, 23 January 2025 (UTC)[reply]

MOS:TWOSTYLES clarifies an exception: "Combined styles are also valid in articles about a term or when significant terms redirect to an article". In the present case, "base" is both a term and a redirect, so it deserves both italics and bold:

...

b n

, is an operation involving two numbers: the base, b, and the exponent or power, n.

Basically, anytime a sentence could be rewritten to use the word "called", a word-as-word is involved:

...

b n

, is an operation involving two numbers: b, called base, and n, called the exponent or power.

The boldface would not be needed only if the redirects were considered "insignificant or minor" (WP:RPLA). However, "base" and "exponent" are key concepts which are likely to be sought after by readers unfamiliar with the subject. "Base" would deserve italics with no bold if it remained as a separate article.

[Caveat: I wrote the above clarification in the MOS a couple of years ago. Since it went undisputed for many years, it is a "generally accepted standard that editors should attempt to follow". Any proposals for further clarifications can be discussed at Wikipedia talk:Manual of Style/Text formatting.] fgnievinski (talk) 03:16, 24 January 2025 (UTC)[reply]

In my opinion adding bold here makes the article worse, and is by no means either a consensus convention on Wikipedia or a requirement of the manual of style. It is distracting but not particularly helpful to readers. "TWOSTYLES" does not seem applicable to this particular situation. Whether a term is redirected here is largely arbitrary and historically contingent – we could easily imagine making many other things redirect to this page, e.g. Repeated multiplication, Fractional power, Multiplication rule (exponentiation), Raise to a power, ..., and these are not "insignificant or minor" topics. Those current red links, just like Base (exponentiation) could easily be turned into redirects, and that would be completely fine. However, bolding the appearance of all of those phrases here would be completely ridiculous and distracting. Similarly, when we just bolded exponentiation, also bolding exponent immediately following is not necessary. Anyone here looking for the word "exponent" is going to trivially find it. –jacobolus (t) 17:45, 24 January 2025 (UTC)[reply]

As for least surprise: I went through the links to base (exponentiation). Most of them were poorly targeted and instead should point at radix. Of the rest, most of those were about the base of a logarithm, which I agree could cause confusion if people end up here instead, since this article doesn't say anything about the base of a logarithm. It would probably be better to put "base" in some explicit glossary page and redirect base (exponentiation) to there instead of redirecting it to this article. –jacobolus (t) 18:46, 24 January 2025 (UTC)[reply]

There's base (mathematics). fgnievinski (talk) 03:31, 28 January 2025 (UTC)[reply]

Article wikilinks are not supposed to point at disambiguation pages.

It might be best to make "base" back into its own article again, direct both base (exponentiation) and base of a logarithm to the same place, and maybe also merge with radix, discussing the "base" of an exponential, a logarithm, a number system, etc. all in one place, since they are still more or less the same idea. –jacobolus (t) 07:12, 28 January 2025 (UTC)[reply]

A middle ground would be creating Base (algebra) as a set index article, which accepts incoming wikilinks, and retargeting the redirects Base of a logarithm and Base of exponentiation (with a see-also link to Base of computation). fgnievinski (talk) 21:37, 28 January 2025 (UTC)[reply]

Base (algebra) seems like a terrible title to me, but this also should not be a "Set index article" (whatever that is). All three are essentially the same idea, not different ideas with the same name. Edit: I think Wikipedia:Broad-concept article is the appropriate guideline page. –jacobolus (t) 22:39, 28 January 2025 (UTC)[reply]

What would be a better title for such a BCA? Base (logarithm and exponentiation) is rather long. Base (mathematics) has other non-related concepts. fgnievinski (talk) 02:30, 29 January 2025 (UTC)[reply]

I strongly oppose to such a BCA, and, by the way, to any new article about bases. Indeed the base of an exponentiation is simply the name given to the first operand of a specific operation, exactly similar to addend, numerator, dividend, ..., none of them having a specific article. The base of a logarithm is the base (common meaning) on which logarithms are built, and the radix of a numeral system is the base on which the system is built. So, a BCA could only be consist on vague considerations on the general meaning of the word "base". The fact that logarithm of base ⁠ $b$ ⁠ and exponentiation of base ⁠ $b$ ⁠ are each the inverse function of the other is well documented in both Logarithm and Exponentiation Moreover, this is more a property of logarithm and exponentiation rather than a property of bases. So, no new article is needed, a such a new article could be confusing. D.Lazard (talk) 10:02, 29 January 2025 (UTC)[reply]

Fair enough. I went through all of the inbound links pointed at Base (exponentiation) and retargeted those about the base of a logarithm to Base of a logarithm (redirects to Logarithm) instead and those about the base of a positional number system to Radix, so hopefully someone who clicks a link on the word "base" won't wind up at exponentiation and get confused. –jacobolus (t) 10:41, 29 January 2025 (UTC)[reply]

Terminology of "power"

The introduction to this page reads:

In mathematics, exponentiation, denoted $b n$ , is an operation involving two numbers: the base, $b$ , and the exponent or power, $n$ .

[...] This binary operation is often read as "b to the power n"; it may also be called "b raised to the nth power", "the nth power of b", or most briefly "b to the n".

Now, correct me if I'm wrong, but strictly speaking, isn't the "power" of an exponential expression its outpot? That is, $p$ in $b n = p$ . My understanding is that refering to such an expression as " $b$ to the power of $n$ " is technically incorrect, and that the "proper" form is those listed after it, better reflecting the logic of "the $n$ th power of $b$ is $p$ " >> " $p$ is the $n$ th power of $b$ " >> " $p$ is a power". " $b$ to the power of $n$ " is still very common, of course, but, assuming I haven't misunderstood something, perhaps this warrants a mention?

Also, not to split hairs, but shouldn't the final example read " $b$ to the $n$ th"? I suppose it's a difficult task to manage linguistic descriptivism and technical prescriptivism in articles of this nature. Kisequé (talk) 06:50, 27 February 2025 (UTC)[reply]

First of all, "prescriptivism" is forbidden in Wikipedia, which has only to report the common usage. I agree that "b to the power of n" is incorrect, but it is not in the quotation of the article. Also, "p is a power" is incorect, while "p is a power of b" is correct. Also, the ordinal (adjective) form is correct before the noun "power", but not for the name of the exponent (after "power" or alone). Finally, "nth" implies that the exponent is a natural number, which is not the general case. So, I do not see anything to change in the article. D.Lazard (talk) 08:05, 27 February 2025 (UTC)[reply]

Powers of one

Using polar form 1 can be exponentiated to become other numbers such as 2, 137, e³, there is not really a limit, so why does this page not talk about the fact that polar form allows such things? 24.83.129.58 (talk) 16:54, 27 May 2025 (UTC)[reply]

Probably, there is a mistake in your reasoning/computation. This is the reason for not talking about in Wikipedia. D.Lazard (talk) 17:07, 27 May 2025 (UTC)[reply]

Cant you just raise 1 to the power of -iln(y)/2npi where n is a non-zero integer, and then exploit 1=e^i2npi, so you get e^(i2npi*(-iln(y)/2npi)), which turns to e^(i×-iln(y)), then you get e^(ln(y)), making it just simplify to y A slice of 8.5397342 (talk) 21:39, 27 May 2025 (UTC)[reply]

The answer is almost certainly no, but it's very hard to read exactly what you are trying to write if you don't use LaTeX for mathematical notation. You might want to look at Mathematical fallacy § Complex exponents. In any event, this page is for discussing improvements to the article, and is not a good venue for miscellaneous discussion about the topic. This kind of question belongs on some other online forum. –jacobolus (t) 23:20, 27 May 2025 (UTC)[reply]

edit request

section: matrices and linear operators "and if A is invertible, then A^{-n} = (A^{-1})^n = (A^n)^{-1}" please add source Username7382287 (talk) 00:58, 4 July 2025 (UTC)[reply]