Trying to show something

**OReilly** · March 15th 2006, 05:49 PM

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?

**kit** · April 15th 2006, 09:17 AM

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.

**OReilly** · April 15th 2006, 01:32 PM

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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