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Thread: Exponent Laws

  1. #1
    Newbie dasswadesh's Avatar
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    Exponent Laws

    I want to know about exponent laws properly. Someone can help me !

    Thanking you
    Swadesh
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  2. #2
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    Re: Exponent Laws

    The "exponent laws" are:

    (a^x)(a^y)= a^{x+ y}
    and

    (a^x)^y= a^{xy}.

    To see why those are true, notice that a^3= (a)(a)(a) and a^2= (a)(a). Multiplying [tex]a^3a^2= [(a)(a)(a)][(a)(a)]= (a)(a)(a)(a)(a)= a^5= a^{2+ 3}[tex] and
    (a^2)^3= (a^2)(a^2)(a^2)= ((a)(a))((a)(a))((a)(a))= a^6= a^{2(3)}
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  3. #3
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    Re: Exponent Laws

    Just two additions. They can be derived from the list HallsofIvy gave you, but I'm listing them for reference.
    1) a^{-n} = \frac{1}{a^n}

    2) a^0 = 1, so long as a \neq 0.

    -Dan
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    Re: Exponent Laws

    And I would add this one as well, which can also be derived from HallsofIvy's post:

     a^{1/n} = \sqrt[n] a
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  5. #5
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    Re: Exponent Laws

    another:
    if a^p = x then p = log(x) / log(a)
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    Forum Admin topsquark's Avatar
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    Re: Exponent Laws

    Quote Originally Posted by DenisB View Post
    another:
    if a^p = x then p = log(x) / log(a)
    Technically that's a logarithm law.

    -Dan
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  8. #8
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    Re: Exponent Laws

    Quote Originally Posted by topsquark View Post
    2) a^0 = 1, so long as a \neq 0.
    You sure?!
    https://www.google.ca/?gws_rd=ssl#q=0%5E0%3D
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  9. #9
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    Re: Exponent Laws

    Quote Originally Posted by DenisB View Post
    yep ...
    Attached Thumbnails Attached Thumbnails Exponent Laws-0-0.png  
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  11. #11
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    Re: Exponent Laws

    Quote Originally Posted by topsquark View Post
    Technically that's a logarithm law.

    -Dan
    "Logarithm" is literally another word for "Exponent". Every logarithm law is also an exponential law hahaha.
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  12. #12
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    Re: Exponent Laws

    last paragraph by the "mathematician" from the above link ...

    There are some further reasons why using 0^0 = 1 is preferable, but they boil down to that choice being more useful than the alternative choices, leading to simpler theorems, or feeling more “natural” to mathematicians. The choice is not “right”, it is merely nice.
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