What's the natural way to express raising to the power of 2 (e.g.5²) and higher exponents (5³ and , 5⁴)?

What's the way/s that native English speakers say this number (52) in words?

Is there a shorter way than "Five to the power of 2"?

For example:

If you take 52 (in words?) and divide it into 5 is equal to 5.

• I believe it is (or used to be) common in American English to say e.g. "five square", the "squared" usage being mainly used in the British English zone. Sep 13 '20 at 18:15
• We say "five squared" and not "five square" to talk about exponention in American English. We would say "five square feet" when talking about a unit of area. Sep 13 '20 at 20:21
• "5^2" is not a "power of 2". Sep 14 '20 at 4:40
• By the way, as someone with a mathematical background, I would take "5^2, divided into 5" as being 5 / 25 = 0.2. You need to say either "divide it by X" or "divide it into X pieces" to clarify which number is the dividend and which is the divisor. Sep 14 '20 at 14:21
• @GrzegorzOledzki no, but it is "five raised to the power of two". "Five squared" or "five to the second" are both more common but not more correct. Sep 14 '20 at 18:01

52 is "five squared".

53 is "five cubed".

54 is "five to the power of four", "five to the power four", "five to the fourth power", "five to the fourth", or "five to the four".

From the comments, it seems some English speakers are unfamiliar with the shorter "to the four" way of saying things, but the following sources (among others) attest to it:

• We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” (see here)
• 54 typically reads as “five to the four” or “five to the fourth”. (see here)
• 104 could be called "10 to the fourth power", "10 to the power 4" or "10 to the 4" (see here)
• No, not necessarily, although at school, kids learn about squares and cubes before they learn about exponents in general, so in non-mathematical circles, "5 squared" is more widely understood, whereas if you say "5 to the power of 2" then many people may look confused. Sep 13 '20 at 16:27
• If you are calculating the area a a 5x5 carpet then 5 squared is normal. Otherwise it doesn't matter much. It's easier to speak and write as 5 squared. However if you are comparing the properties of different powers x to the power n is perfectly acceptable. Cross-posted with rjpond's comment. Sep 13 '20 at 16:30
• FWIW I'm a mathematician and BrE speaker and "to the power of n" sounds odd (although not incorrect) to me; I almost never hear anybody include the "of". Sep 14 '20 at 9:17
• I wonder if anyone has ever seriously used "five tesseracted" Sep 14 '20 at 9:37
• @EspeciallyLime: Are you sure? I’m also a mathematician and BrE speaker, and “5 to the power 4” without “of” sounds much less standard to me. Normally (among STEM professionals/students) I’d just say “5 to the 4th” without “power”, but if including “power” (e.g. to be clearer to a layperson) then I would always say “…power of 4”, and my intuition is that that’s more common than “power” without “of”.
– PLL
Sep 14 '20 at 10:45

"Power of n" indicates that n is the base. To indicate that it's the exponent, the phrasing is "nth power". So, for instance, 5^2 is the second power of 5, 5 raised to the second power, or 5 to the second. The second power is usually referred to as squared and the third power as cubed.

• On its own, "power of 5" would mean 2 was the base, but the form the OP used was "to the power of 5", which is commonly used as an equivalent of "to the 5th power", at least here in the UK. Sep 14 '20 at 15:08
• That first sentence looks wrong to me. In a context like Two to the power [of] three, 2 is the "base" and 3 is the "exponent" (or "power"), as OP already knows. And so far as I'm concerned, it's not idiomatic anywhere to refer to 5 to the second. Sep 14 '20 at 16:21
• @FumbleFingersReinstateMonica "five to the second" is a common way to say 5^2, at least in the US. Like page 131 of this book says: google.com/books/edition/The_Everything_Guide_to_Pre_Algebra/… or page 59 of this one: google.com/books/edition/… Sep 14 '20 at 16:41
• "power of two" means two is it base in the sentence "eight is a power of two" but it's not incorrect to say "eight is two to the power of three". Sep 14 '20 at 17:28
• Well, that first sentence is correct, but that's not the phrase the question used. 128 is indeed a power of 2, but 5 to the power of 2 is 25. In the first one, 2 is the base, in the second, it's the exponent. That's two different phrases, similar, but not the same. Sep 14 '20 at 20:04

These are obscure, and probably not understood, but are real words:

zenzizenzic - 4th power

zenzic cube - 6th power

zenzizenzizenzic - 8th power.

(IIRC, Arabic in origin, through German to English. Lit. "square of the square", "square of the cube", "square of the square of the square".)

Don't have my source with me.

• I'm not sure an obsolete and obscure mathematical notation term falls under "a natural way to express 5²". Feb 3 '21 at 20:34