# saying 4³ [four powered three / four power three?]

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#### Godo159

##### Senior Member
Hi, I'm a teacher in a bilingual program, and we have a doubt with maths language. I know that you can read aloud 4³ as "four cubed", "four raised to the third power", and "four to the third". Also, SolAguila told me that he says "four to the power of three".

My question is, can you read it as "four powered three" or "four power three", too? What is the simplest form that you used when you were at school?

• #### PaulQ

##### Senior Member
"Can you read it as "four powered three" or "four power three", too?" No, you can't.
What is the simplest form that you used when you were at school? "Four cubed."

#### Florentia52

##### Modwoman in the attic
In AE, we coud say "four to the power of three," as you have discovered. I have never heard "four powered three" or "four power three." Those would sound odd to me.

We always said "four cubed" when I was in school, but that was some time ago.

#### heypresto

##### Senior Member
No, I'm afraid we don't use either "four powered three" or "four power three".

All the other ways you know for describing
4³ are fine, with "four cubed" being the simplest.

Cross-posted.

#### waltern

##### Senior Member
The form I heard most often (setting aside "cubed" or "squared") was along the lines of "four to the third" - for example when using scientific notation, 2.1x10^-6 would be read "two point one times ten to the minus sixth".

#### PaulQ

##### Senior Member
Interesting, I would take 2.1x10^-6 as "two point one times ten to the minus six.", although 4^4 would be "four to the fourth." -> "X^Y = X to the Yth" For me, the 'minus' causes the number to revert to the cardinal.

#### Godo159

##### Senior Member
Thank you very much, I didn't realise this would turn out to be such a popular issue. So, leaving aside the possibility of "four cubed", which only works for "squared" or "cubed", all other powers such as 54 should be read as "five (raised) to the power of four" or "five to the fourth (power)", and there are no other possibilities, right?

What about really big numbers, do you still have to read 123144 as "a hundred and twenty-three to the hundred and forty-fourth", or do you prefer "... to the power of a hundred and forty-four"?

#### PaulQ

##### Senior Member
"a hundred and twenty-three to the hundred and forty-fourth", or do you prefer "... to the power of a hundred and forty-four"? Both work. The chances of your having to say this sort of expression are slim unless you associate with mathematicians or physicists, and they will understand whichever you say.

#### pob14

##### Senior Member
I have always used the ordinal for all powers: three to the fifth, seventeen to the twenty-fifth, ten million to the three billionth. Sometimes I say "power" at the end, but never "the power of . . . ." That sounds very strange to me.

And if I ever said "to the minus sixth" (or six, or anything else), instead of "the negative sixth," my third grade teacher would come back from the dead, hunt me down, and beat me senseless. "Minus," she told us, was reserved for the subtraction operator, never for the sign of a number.

#### Godo159

##### Senior Member
Thank you all so much for your help. I am indeed associating with mathematicians: we have a bilingual programme in our school, and things like these are difficult to find out with only a dictionary. These forums have been a great help on many occasions. Keep up the good work!

#### entangledbank

##### Senior Member
There was another thread on this yesterday morning, and there have been others, I'm sure. I'll just repeat here what I said in http://forum.wordreference.com/showthread.php?t=2728655:

For 2 and 3, we say x squared and x cubed. For larger numbers, you can say x to the power of five, or x to the fifth power, or just x to the fifth. As a mathematician I often have to use powers that don't have ordinal forms: I say these as x to the minus 1, x to the pi, x to the (a + b), and so on. So even for ordinary integers I usually just say x to the five. But perhaps you should use one of the three forms I mentioned earlier.

#### Edinburgher

##### Senior Member
"Minus," she told us, was reserved for the subtraction operator, never for the sign of a number.
Long may she turn in her grave. Though we refer to these things as "negative numbers", in practice it's almost universal to say "minus" both for subtraction and negation. I do baulk at "minus numbers", which is alarmingly common.

Q: What's three minus five?
A1: Minus two.
A2: Negative two. (technically perhaps , but in practice almost )

To get back to powers, I would not normally include "of" after "power".
When the word "power" is retained:
The ordinal is required if the exponent precedes it: three to the fifth power.
The cardinal is required if the exponent follows it: three to the power five.
When the word "power" is omitted, the ordinal is optional, because I see it as an elision of wither of the above.
For me, "minus" is neither necessary nor sufficient to cause the ordinal to revert to the cardinal. I'm happy with all these:
three to the five,
three to the minus five,
three to the fifth,
three to the minus fifth.

But in the ordinal cases, care is needed to avoid confusion with a fractional exponent. Normally, "two to the twelfth" will mean 4096, but if discussing frequency ratios of semitones, it might mean 1.059463, being an elision of "two to the power a twelfth", 2^(1/12), also known as the twelfth root of two.

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