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Math Help - indices laws negative powers

  1. #1
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    indices laws negative powers

    hi all
    i got some h/w for negative powers teatcher said :
    X^-a = 1/X^a
    why is that?
    thanks.....
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  2. #2
    o_O
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    Raising a number to -1 will produce its reciprocal: {\color{red}x}^{-1} = \frac{1}{{\color{red}x}} (this is just how it is defined)

    So: \underbrace{x^{-a} = \left({\color{red}x^{a}}\right)^{-1}}_{\text{Since: } \displaystyle a^{bc} = \left(a^{b}\right)^{c} } \! = \frac{1}{{\color{red}x^{a}}}
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  3. #3
    Senior Member bkarpuz's Avatar
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    Because, it is defined to be
    x^{a}x^{b}=x^{a+b},
    letting b=-a, we get
    x^{a}x^{-a}=x^{a-a}=x^{0}=1,
    which indicates
    x^{a}=\frac{1}{x^{-a}}\text{ or equivalently }x^{-a}=\frac{1}{x^{a}}
    privided that x\neq0.
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  4. #4
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    Smile

    In english plz ??
    That be a great help scince im only startin gcse's
    thanks all...
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by spik31 View Post
    In english plz ??
    That be a great help scince im only startin gcse's
    thanks all...
    I think this is a d**n cheek, try posting in English yourself.

    RonL
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