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# When does this law of exponents not work?

Normally, one of the laws of exponents tells us that $$a^{bc} = \left(a^b\right)^c$$.

However, there are some cases (when $$a,b,c$$ are allowed to be non-integers) when this formula does not work. For example, $$(i^4)^{\sqrt{2}} \neq i^{4\sqrt{2}}$$.

Find the set of all ordered triples $$(a,b,c)$$ where $$a,b,c \in \mathbb{C}$$ such that $$a^{bc} \neq \left(a^b\right)^c$$.

Note by Ariel Gershon
2 years ago