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Math Help - Rational Exponent

  1. #1
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    Rational Exponent

    Really sorry for asking so many questions but my test is about to begin and I'm running into quite a few problems on my review...
    This time, it is rational exponents.

    Rational Exponent-codecogseqn-6-.png


    The answer is apparently:
    Rational Exponent-codecogseqn-5-.png



    **I don't know where they got 23/3 from. I know the 56 is from 7*8, but that's pretty much all I could understand? Multiplying the exponents always gives me an 8. Mind telling me what I'm doing wrong? Might it be a typo?


    Thank You,
    Azusa.
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  2. #2
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    Re: Rational Exponent

    Exponents are added, but only when the base is the same: x^\alpha\cdot x^\beta=x^{\alpha+\beta}.
    Thanks from Azusa
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  3. #3
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    Re: Rational Exponent

    Quote Originally Posted by Azusa View Post
    Really sorry for asking so many questions but my test is about to begin and I'm running into quite a few problems on my review...
    This time, it is rational exponents.

    Click image for larger version. 

Name:	CodeCogsEqn(6).png 
Views:	12 
Size:	1.3 KB 
ID:	23750


    The answer is apparently:
    Click image for larger version. 

Name:	CodeCogsEqn(5).png 
Views:	12 
Size:	984 Bytes 
ID:	23749



    **I don't know where they got 23/3 from. I know the 56 is from 7*8, but that's pretty much all I could understand? Multiplying the exponents always gives me an 8. Mind telling me what I'm doing wrong? Might it be a typo?


    Thank You,
    Azusa.
    You're not supposed to multiply the exponents. You're supposed to know that \displaystyle \begin{align*} a^m \cdot a^n = a^{m+n} \end{align*}, so you're supposed to add them.
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  4. #4
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    Re: Rational Exponent

    Ahh... Right. I'm so nervous I had forgotten other (correct) methods. Thank You!!!!
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