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Exponents notation

  1. Feb 3, 2005 #1
    I have a small question about exponents: when we write a^x (i will write it this way but i talk about the traditional notation) this means that the base is only a? I mean that if we have ba^x or -a^x then then these are equal to b(a^x) and -(a^x) ? These are also because of the order of operations? Generally if we want a "whole expression" to be raised in a power then we have to write it in a parentheses? So for example -2^2=-4 but (-2)^2=4 ?
    So we calculate this exponent and then do multiplications, divisions etc..?
  2. jcsd
  3. Feb 3, 2005 #2


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    i agree with you. i.e. i use the notation as you have said.

    one remark: if you intend also to raise your base to fractional powers, like 1/2,

    then you are particularly advised that, if you are dealing with real numbers, the base should be positive, since (-1)^*1/2) is not a real number.

    i.e. in ordinary calculus courses about real numbers, in first and second year in most US universities, a^x should only be used when a is positive (or zero). I.e. if you intend a^x to be a function defiend for all real numbers x, or even for all rational numbers x, then a should be positive.
  4. Feb 3, 2005 #3


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    Yes, it is based on "order of operations". -22= - 2*2= -4 because exponentiation takes precedence: it is -(2)(2). (-2)2= (-2)(-2)= 4 because of the parentheses.
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