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Math Help - Need help with multiply exponents!

  1. #1
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    Question Need help with multiply exponents!

    Ok, watch the exponents in this problem, thanks!
    How does (1+x)2(√1+x)^ = 2(√1+x)^3/2
    when you multiply the following exponents (2)(-1/3) you get (-2/3).
    Both are multiplying rational exponents, but two are doing it very differently. One has to be wrong, but which?
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  2. #2
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    Re: Need help with multiply exponents!

    Quote Originally Posted by EJdive43 View Post
    Ok, watch the exponents in this problem, thanks!
    How does (1+x)2(√1+x)^ = 2(√1+x)^3/2
    when you multiply the following exponents (2)(-1/3) you get (-2/3).
    Both are multiplying rational exponents, but two are doing it very differently. One has to be wrong, but which?
    (1+x)2(√1+x)^ = 2(√1+x)^3/2

    I think you have one too many exponents.

    correction ...

    (1+x) \cdot 2\sqrt{1+x} = (1+x) \cdot 2(1+x)^{1/2} = 2(1+x)^{3/2}
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  3. #3
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    Re: Need help with multiply exponents!

    I understand that, but in a problem like (8x^3/4y^2)^ -1/3, where I'm ask to simplify, when I multiply the two exponents (2)(-1/3) I get 6/3 on on the answer sheet it says it's 2/3. http://www.wtamu.edu/academic/anns/m...ut5_ratexp.htm (example 5)
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  4. #4
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    Re: Need help with multiply exponents!

    Why did they multiply (2)(-1/3) to get (-2/3) when that not how you multiplied (1+x)*2(/1+x)^1/2 to get 3/2 as a result?
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    Re: Need help with multiply exponents!

    Quote Originally Posted by EJdive43 View Post
    Why did they multiply (2)(-1/3) to get (-2/3) when that not how you multiplied (1+x)*2(/1+x)^1/2 to get 3/2 as a result?
    {\left( {\frac{{8{x^3}}}{{4{y^2}}}} \right)^{\tfrac{{ - 1}}{3}}} = {\left( {\frac{{{y^2}}}{{2{x^3}}}} \right)^{\tfrac{1}{3}}} = \frac{{{y^{\tfrac{2}{3}}}}}{{{2^{\tfrac{1}{3}}}x}}
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  6. #6
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    Re: Need help with multiply exponents!

    How did you work that out?
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  7. #7
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    Re: Need help with multiply exponents!

    Nvm I did, but how did you get 2/3 for y
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    Re: Need help with multiply exponents!

    Quote Originally Posted by EJdive43 View Post
    Nvm I did, but how did you get 2/3 for y
    \left( 2 \right)\left( {\frac{1}{3}} \right) = \frac{2}{3}
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  9. #9
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    Re: Need help with multiply exponents!

    Don't you multiply the exponents which means your going to add? For example, (2)(-1/3) we will add the exponents which will be written as 2+-1/3, right? Isn't that what Skeeter did with the equation above?
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    Re: Need help with multiply exponents!

    Quote Originally Posted by EJdive43 View Post
    Don't you multiply the exponents which means your going to add? For example, (2)(-1/3) we will add the exponents which will be written as 2+-1/3, right? Isn't that what Skeeter did with the equation above?
    \text{It is a rule that }{\left( {{x^a}} \right)^b} = {x^{ab}}\text{ so applying that rule we get }\left( {{y^2}} \right)^{\frac{1}{3}}} = {y^{\frac{2}{3}}}~.
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  11. #11
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    Re: Need help with multiply exponents!

    do you understand that

    x^a \cdot x^b = x^{a+b} and (x^a)^b = x^{ab}

    are two completely different rules for exponents?
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