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How do you say the mathematical function in English:

x^y (or xy)

For example, how do you say

2^16 (or 216)

I know ^ means 'power' or 'exponentiate', but that is the name of the operation, not how you pronounce its use.

If y = 2, it is 'x squared', y=3 then 'x cubed'. What if y is some other arbitrary number?

RegDwigнt
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daisy
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    This is explained in the wiktionary entry for power (see meaning 8) – Matt E. Эллен Jul 11 '12 at 08:31
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    The obvious thing to say is 65536. – James Waldby - jwpat7 Jul 11 '12 at 15:36
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    Could someone explain how, exactly, this question is off topic? The FAQ states pronunciation questions are on topic, does not explicitly say anything to indicate how to talk about math in English is off topic, it seems fair to me that this might be said differently in English than other languages (almost certainly so), and there's no reason to automatically suspect the questioner is non-native. So why close it? – Questioner Jul 17 '12 at 05:00
  • Note that the notation x^y derives from BASIC, and is not seen in FORTRAN, where the power operator is ** not ^, nor in languages derived from C, since they already use ^ for bitwise xor. So you will some people write x**y for your x^y. – tchrist Aug 01 '12 at 13:25
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    For clarification, the ^ symbol is also called the caret symbol. – Desura Aug 03 '12 at 18:49
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    Cross-linking: How is "e^x" read aloud? over at Maths, our sister site for people studying math at any level and professionals in related fields. – RegDwigнt Oct 10 '12 at 21:45

4 Answers4

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The references say "two to the sixteenth power" or "two to the power of sixteen" but that is only done in very formal speech. Ironically, in actual mathematical usage, the formal pronunciation is not that common.

The more common way to say it (in math class or in a mathematical presentation) is a ellipsis of the first:

two to the sixteenth

or just as commonly

two to the sixteen

depending on how rapid speech you are using.

Of course there are some special cases: x2 is "x squared", x3 is "x cubed". x1 or x0 are mathematically jarring if written alone (they are often, when mathematically allowed, written just "x" and "one"), but if forced would be "x to the one" and "x to the zero", never as an ordinal (it is a solecism to say "x to the first" and way too informal to say .

For example, a polynomial x109 + 9x5 − 2x2 is most likely pronounced:

x to the hundred and nine plus nine x to the fifth minus two x squared.

(or "hundred and ninth"; both are equally possible here). If it were x101 — see discussion here —, you just don't say "one hundred first".)

If variables are involved, the ordinal is not used. xy is

x to the y

(that is, not appending the ordinal suffix '-th').

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Mitch
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    With respect, I entirely disagree with your assertion that "two to the power of sixteen" is somehow formal. It just isn't. Additionally, I might say "two to the sixteenth", but while I've learned that there's always someone out there who will say things in a way I never imagined, I would never say "two to the sixteen", and I've never heard anyone else use that. – Questioner Aug 01 '12 at 15:59
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    @DaveMG: "two to the sixteen" only sounds odd in a non-mathematical context. I'm willing to bet that if you heard it in a math class, you wouldn't even blink; and in fact you might even hear it as "sixteenth", i.e. your mind would automatically supply the ordinal. – Marthaª Aug 01 '12 at 17:07
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    @Marthaª: I don't think it matters what anyone claims another seems to say, or what anyone thinks they hear. "Depending on how rapid speech you are using" is convenient way of justifying anything said. Speaking fast enough, one might say "twot'thsixeeth", but so what? – Questioner Aug 01 '12 at 17:15
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    @DaveMG I find your comments unnecessarily contrarian. Describing "Two to the power of sixteen" as a more formal version of "two to the sixteenth" is a perfectly valid and natural way to convey the notion that one form is preferred over the other in a conversational context. Obviously both forms fully specify a mathematical operation, and in that sense, they are actually both quite formal. Furthermore, just because you haven't seen it, doesn't mean that some people, even competent mathematicians, don't use an ordinal in the short form sometimes. – Cameron Aug 01 '12 at 18:04
  • @Cameron: Can you prove that "one form is preferred over the other in a conversational context"? Otherwise, it doesn't matter how natural it is to convey the notion, the notion itself is no more or less opinion than what I'm saying, and I disagree with your opinion on the matter. – Questioner Aug 02 '12 at 03:49
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    X raised to the 0th power is never pronounced 1, although it is 1 for every X. X raised to the Y power is also possible to be said. – speedyGonzales Aug 02 '12 at 06:24
  • @speedyGonzales: you're right, it is never pronounced that way. But often it will be rewritten/simplified. – Mitch Aug 02 '12 at 13:04
  • @DaveMG Since you have yet to provide any evidence that my opinion is wrong, here's a real experiment you can run: use Google or YouTube and search for lectures from, e.g., algebra classes on exponents. Grab the first 20 or so you can find. Transcribe them and count the instances of each usage (many are already transcribed). If you can show that the long form is at least as frequent, I'll gladly admit that I was wrong (but I can't speak for the writers of the two most upvoted answers here that said the same thing). Please reply with an invitation to chat, if you choose to. – Cameron Aug 02 '12 at 15:57
  • @Cameron: Of course I haven't provided evidence that your opinion is wrong, because no one can prove a negative. But will I do the homework you assigned to me? No, because it's not my job to prove you right. You either present evidence, or you don't. Asking others to do the work for you... that's just the sign that this has devolved into one of those pointless internet debates that people get into sometimes. Here's my bottom line: I disagree with you. You disagree with me. The potential for an objective answer is close to zero. Thanks for your opinions, and take care. – Questioner Aug 03 '12 at 03:40
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I would use two raised to the sixteenth power which is the full version. Although when people are saying a big numeral expression they skip it to two to the sixteenth.

speedyGonzales
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"Two to the power of sixteen."

Questioner
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You could also say Two to the sixteenth

Noah
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Rover_KE
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