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I have a question about power rules, we have f(m,n) :

$\ a^{(m-n)}= \frac{a^m}{a^n}$

which is separable. What about:

$\ a^{|m-n|}= ?$

Is it separable? I want f(m,n)=f(n,m)

Thanks.

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    $\begingroup$ What is your initial thoughts? What do you know about absolute values? $\endgroup$ – WaveX Mar 6 at 14:56
  • $\begingroup$ Maybe I should change my question. $\endgroup$ – Ana.IM Mar 6 at 15:00
  • $\begingroup$ Depends on what $m,n$ are. If they $\in\Bbb R$ (basically any ordered field), you could write it as $\dfrac{a^{\max(m,n)}}{a^{\min(m,n)}}$. For fields like $\Bbb C$ which are not ordered, I don't think any similar simplification exists. $\endgroup$ – learner Mar 6 at 15:05
  • $\begingroup$ Also, I think you might want to read over the definition of "commutative"; it's not what you seem to think it is. $\endgroup$ – learner Mar 6 at 15:07
  • $\begingroup$ Thank you, my problem is that the min and max are unknown. I want f(m,n)=f(n,m) $\endgroup$ – Ana.IM Mar 6 at 15:09

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