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Math Help - Trying to show something

  1. #1
    Senior Member OReilly's Avatar
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    Trying to show something

    Can someone tell me is this right? Its about rational exponents.

    a^{\frac{m}{n}}  < a^{\frac{p}{q}} is true only if \frac{m}{n} < \frac{p}{q} for a>1

    I will show that this is true.

    If we divide both sides with a^{\frac{m}{n}} we get
    1 < \frac{{a^{\frac{p}{q}} }}{{a^{\frac{m}{n}} }}
    which is 1 < a^{\frac{p}{q} - \frac{m}{n}}

    a^{\frac{p}{q} - \frac{m}{n}}  > 1 is true only if \frac{p}{q} - \frac{m}{n} > 0 so then it must be \frac{p}{q} > \frac{m}{n} so then a^{\frac{m}{n}}  < a^{\frac{p}{q}} its true.

    Is that ok?
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  2. #2
    kit
    kit is offline
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    It's been a while since I did proofs of this kind, but looking at what at you've got - it looks to be ok. Nice logical methodology etc.

    One thing to point out though - if this is a written assignment, I would make your explanations clearer (such as a raised to the 0 = 1, hence the exponents have to be greater than 0).

    Just a written explanation like this whilst going through the process makes it easier to read, and also to follow through logically.
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  3. #3
    Senior Member OReilly's Avatar
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    Quote Originally Posted by kit
    One thing to point out though - if this is a written assignment, I would make your explanations clearer (such as a raised to the 0 = 1, hence the exponents have to be greater than 0).
    You are right, that must be written. My mistake.
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