# Thread: Trying to show something

1. ## 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?

2. 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.

3. 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.