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Math Help - Help with Exponent Expression

  1. #1
    Member cmf0106's Avatar
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    Help with Exponent Expression

    I am going to post the entire problem & its solution. I am confused with one particular step in working towards the solution.

    (2x^3+4)^{-6}(2x^3+4)^4=(2x^3+4)^{-6+4} =(2x^3+4)^{-2} = \frac{1}{(2x^3+4)^2}

    How are the two " (2x^3+4)" combined to form one (2x^3+4)? Is it because they both have the same base therefore just add the exponents together? Im thinking that must be correct, otherwise I wouldnt be adding these exponents to begin with.
    Last edited by cmf0106; August 17th 2008 at 07:27 AM.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by cmf0106 View Post
    I am going to post the entire problem & its solution. I am confused with one particular step in working towards the solution.

    (2x^3+4)^{-6}(2x^3+4)^4=(2x^3+4)^{-6+4} =(2x^3+4)^{-2} = \frac{1}{(2x^3+4)^2}

    How are the two " (2x^3+4)" combined to form one (2x^3+4)? Is it because they both have the same base therefore just add the exponents together? Im thinking that must be correct, otherwise I wouldnt be adding these exponents to begin with.
    Remember this rule of exponents:

    x^a \cdot x^b = x^{a+b}

    This explains:

    (2x^3+4)^{-6}(2x^3+4)^4=(2x^3+4)^{-6+4}

    And then, simply add the exponents-6+4 to get:

    (2x^3+4)^{-2}

    And finally, use the reciprocol of the above to reach the conclusion with a positive exponent:

    \frac{1}{(2x^3+4)^2}
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