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What does it mean if I raise a power to the power etc?

  1. May 21, 2010 #1
    What is the result of a number raised to the power of the number raised to a power.

    I.e. 2^2^2?
     
  2. jcsd
  3. May 21, 2010 #2

    Mark44

    Staff: Mentor

    This expression is evaluated from right to left, as if parentheses were placed like so:
    2^(2^2) = 2^4 = 16.

    For this problem, the order isn't important, since (2^2)^2 = 4^2, also equals 16. For other problems with different numbers, thought, you can get different results.

    For example, 5^2^3 = 5^(2^8) = 5^8 = 390625.

    If you evaluate in the wrong order, you get (5^2)^3 = 25^3 = 15625.
     
  4. May 21, 2010 #3
    Thats great thanks
     
  5. May 21, 2010 #4

    DaveC426913

    User Avatar
    Gold Member

    Too soon to introduce him to "[URL [Broken] Number[/URL]? :biggrin:
     
    Last edited by a moderator: May 4, 2017
  6. May 21, 2010 #5

    Mark44

    Staff: Mentor

    Might be!
     
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