# How Absolute changes power rules?

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

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

$$\ a^{|m-n|}= ?$$
• 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. – learner Mar 6 at 15:05