Results 1 to 9 of 9

Math Help - Exponents

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    78

    Question Exponents

    Why is 5-⅔ (5 raised to the power of -2/3) equal to 1/5⅔ (1 divided 5 raised to the power of 2/3)? I mean to say how does the negative sign of the exponent ⅔ change to positive when 5-⅔ (5 raised to the power of -2/3) is inversed?


    Thanks,

    Ron
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,569
    Thanks
    1428
    Quote Originally Posted by rn5a View Post
    Why is 5-⅔ (5 raised to the power of -2/3) equal to 1/5⅔ (1 divided 5 raised to the power of 2/3)? I mean to say how does the negative sign of the exponent ⅔ change to positive when 5-⅔ (5 raised to the power of -2/3) is inversed?


    Thanks,

    Ron
    Because a^{-n} = \frac{1}{a^n}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    78
    Quote Originally Posted by Prove It View Post
    Because a^{-n} = \frac{1}{a^n}.
    But why is a^{-n} = \frac{1}{a^n}?

    Ron
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by rn5a View Post
    But why is a^{-n} = \frac{1}{a^n}?

    Ron
    Because it is. You can explain it using this formula :

    \frac{a^m}{a^n} = a^{m - n}

    In our case, m = 0 because a^0 = 1, and thus it follows that :

    \frac{a^0}{a^n} = a^{0 - n}

    Which is equivalent to :

    \frac{1}{a^n} = a^{-n}

    Now, you are probably going to ask us why \frac{a^m}{a^n} = a^{m - n}. To this I will answer : "Why does 1 + 0 = 1 ?".
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2009
    Posts
    78
    Quote Originally Posted by Bacterius View Post
    Because it is. You can explain it using this formula :

    \frac{a^m}{a^n} = a^{m - n}

    In our case, m = 0 because a^0 = 1, and thus it follows that :

    \frac{a^0}{a^n} = a^{0 - n}

    Which is equivalent to :

    \frac{1}{a^n} = a^{-n}

    Now, you are probably going to ask us why \frac{a^m}{a^n} = a^{m - n}. To this I will answer : "Why does 1 + 0 = 1 ?".
    Thanks mate....that was a great explanation. BTW why is 1 + 0 = 1?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by rn5a View Post
    Thanks mate....that was a great explanation. BTW why is 1 + 0 = 1?
    Because it is xD
    It's an axiom. Mathematics are based on this assumption along with some others. You don't prove this. You assume it.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,569
    Thanks
    1428
    Quote Originally Posted by Bacterius View Post
    Because it is xD
    It's an axiom. Mathematics are based on this assumption along with some others. You don't prove this. You assume it.
    Actually, the reason you don't prove it is because it's obvious. Therefore you don't assume it, you know it. Because it's obvious.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member Chokfull's Avatar
    Joined
    May 2009
    From
    Neverland
    Posts
    108
    Thanks
    1
    I wouldn't say "It's just obvious". When you have 5^2, it means 1*5*5. When the exponent, which means the number of 5s you multiply the 1 by is negative, you start dividing. Therefore, 5^{-1}=\frac {1} {5}
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,569
    Thanks
    1428
    Quote Originally Posted by Chokfull View Post
    I wouldn't say "It's just obvious". When you have 5^2, it means 1*5*5. When the exponent, which means the number of 5s you multiply the 1 by is negative, you start dividing. Therefore, 5^{-1}=\frac {1} {5}
    I was talking about the 1 + 0 = 1 statement
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Exponents and Log Help!!
    Posted in the Algebra Forum
    Replies: 17
    Last Post: August 14th 2011, 10:21 AM
  2. exponents
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 17th 2010, 08:37 AM
  3. Need help with exponents
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: August 30th 2008, 05:07 AM
  4. Exponents
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 18th 2008, 09:51 PM
  5. exponents
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 28th 2008, 01:53 PM

Search Tags


/mathhelpforum @mathhelpforum