1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Are 'power', 'index' and 'exponent' exact synonyms

  1. Sep 7, 2009 #1
    Can you please help me sort out my terminology?

    Are 'power', 'index' and 'exponent' exact synonyms, even thogh they tend to be used in different contexts? If a^x gives 'exponential growth' is the growth described by x^a also properly called 'exponential'? If not, what is it called?


  2. jcsd
  3. Sep 7, 2009 #2


    User Avatar
    Science Advisor

    Re: Terminology

    I would consider "power" and "exponent" to be basically the same- "exponent" being a little more formal than "power". Our British friends use "index" to mean "exponent" but we Americans do not. To us an "index" is simply a "label" (as on a vector or tensor) and can be either a superscript of a subscript.

    "Exponential growth" on the other hand refers to the "exponential function", ex or variations on that such as ax= ex ln(a). Something like xa is a "polynomial function" if a is a positive integer, a "rational function" if a is a negative integer, a "radical function" if a is a fraction, and a "transcendental function" if a is irrational.
  4. Sep 7, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    Re: Terminology


    Often, in modelling, to utilize a function:
    is called to use a "power law". (C, a constants to be empirically determined).
  5. Sep 7, 2009 #4


    User Avatar
    Science Advisor

    Re: Terminology

    Yes that's the way I refer to them.

    [itex]f(x) = a^x [/itex] : an exponential.

    [itex] f(x) = x^a [/itex] : a power (of x).
  6. Sep 7, 2009 #5
    Re: Terminology

    Thanks for those replies. Can you use "exponentiation" as a noun, to go with "addition" and "multiplication" for example, to generally describe the general process of raising one number to the power of another, then, or should it be reserved for raising e or some other number to the power of x?

    Also, the phrase "exponential growth" is a common one, but what would you put in the bracket in "( ) growth" if the growth was described by, say, a polynomial function?
  7. Sep 7, 2009 #6
    Re: Terminology

    These are the distinctions as I know them:

    A "power" is an operation also known as exponentiation, as in the third power of 2 is 8.

    The "exponent" is the argument in the superscript of a power - then n in an. It is also the "index" of the power in the same way as n is the index of the radical [tex]\sqrt[n]{a}[/tex].

    For a constant:

    [itex]f(x) = a^x[/itex] is an exponential function.

    [itex]g(x) = x^a[/itex] is a power function.

    I hope this helps.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook