Exponent Simplification

Algebra Level 3

\[\Large{\text{Is }\left(2^\color{red}{a}\right)^{\color{blue}{b}} \text{ } = \text{ } 2^{\color{red}{a}+\color{blue}{b}} \quad \text{ or } \quad 2^{\color{red}{a}\color{blue}{b}} \text{ ?}}\]

To see which simplification is correct, you plug in specific numbers \(\color{red}{a}=A\) and \(\color{blue}{b}=B\), but somehow both proposed simplifications give the same answer: \(64.\) Find \(\left(A-B\right)^2.\)