Repeated Exponentiation doubt

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I have a somewhat silly doubt about this seemingly basic topic - repeated exponentiation. I've got very little experience regarding this, so please hear me out.

We know that one of the properties of exponents are as follows : $$a^{m^n} = (a^m)^n = a^{mn}$$

However, this property is no longer true for more than two exponents. In that case we have to evaluate them from the highest power to the base.

We have here, $a^{m^{n^p}} \ne a^{mnp}$.

Instead what we do is : $$a^{m^{n^p}} = a^{(m^{(n^p)})}$$

Wikipedia calls this 'right associative' but I don't know what that means here. WHy do we evaluate repeated exponents in this way, and not the other way ?