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Math Help - Exponent question

  1. #1
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    Exponent question

    what is the easiest way to remember the order of operations over a lifetime.
    What different rule when working out exponents any feedback ?
    Last edited by C++programmerinCali; January 5th 2009 at 06:46 AM. Reason: Incorrect wording.
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  2. #2
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    Quote Originally Posted by C++programmerinCali View Post
    How do YOU keep the rules of exponents straight ?

    What different ways do try to apply this rule when working out exponents any feedback ?
    It's through practice.

    Wikipedia gives a comprehensive overview of the rules of working with exponents: Exponentiation - Wikipedia, the free encyclopedia

    And most of these are fairly intuitive. For example x^{m-n} is equivalent to multiplying x by itself m times and then dividing by x n times, resulting in x^m/x^n. Or for instance x^0 = x^{m-m} = x^m/x^m = 1.
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  3. #3
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    Hello, C++programmerinCali!

    How do YOU keep the rules of exponents straight ?

    When I was first learning these Rules, I came up with a "picture" of what was happening.
    It was quite primitive (and even childish), but it worked for me.


    Think of the "heirarchy" of some basic operations.

    First we learned to Count objects: . 1,2,3\:\hdots

    Then came Addition, which is "repeated counting."
    . . (and Subtraction is "repeated take-away.")

    Then came Multiplication, which is "repeated addition."
    . . (and Division is "repeated subtraction.")

    Finally, we learned Powers, which is "repeated multiplication."
    . . (and Roots are "repeated division.")


    So, written in order, we have:

    . . \text{Counting } \Rightarrow \begin{Bmatrix}\text{ Addition }\\ \text{ Subtraction}\end{Bmatrix} \Rightarrow \begin{Bmatrix}\text{ Multiplication} \\ \text{Division } \end{Bmatrix} \Rightarrow \begin{Bmatrix}\text{ Powers } \\ \text{ Roots} \end{Bmatrix}



    With the Rules of Exponents, we reverse the order . . .

    . . \text{Powers } \underbrace{\Longrightarrow}_{(a^m)^n = a^{mn}} \text{ Multiplication } \underbrace{\Longrightarrow}_{a^m\cdot a^n = a^{m+n}} \text{ Addition}

    . . \text{Roots } \underbrace{\Longrightarrow}_{(a^m)^{\frac{1}{n}} = a^{\frac{m}{n}}} \text{ Division } \underbrace{\Longrightarrow}_{\frac{a^m}{a^n} = a^{m-n}} \text{ Subtraction}



    I really didn't visualize these diagrams.
    I noted that, for exponents, we "step down" an operation.
    (For example, to multiply, we add exponents . . . and so on.)

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