Exponent Simplification

Algebra Level 3

Is (2a)b = 2a+b or 2ab ?\Large{\text{Is }\left(2^\color{#D61F06}{a}\right)^{\color{#3D99F6}{b}} \text{ } = \text{ } 2^{\color{#D61F06}{a}+\color{#3D99F6}{b}} \quad \text{ or } \quad 2^{\color{#D61F06}{a}\color{#3D99F6}{b}} \text{ ?}}

To see which simplification is correct, you plug in specific numbers a=A\color{#D61F06}{a}=A and b=B\color{#3D99F6}{b}=B, but somehow both proposed simplifications give the same answer: 64.64. Find (AB)2.\left(A-B\right)^2.

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