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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

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