# 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 $$\left(A-B\right)^2.$$

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