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2021 AMC 12A Question 9

AMC12 · 2021 AMC 12A

Question 9

Which of the following is equivalent to $$
\begin{aligned} &(2 + 3)(2^2 + 3^2)(2^4 + 3^4) \\ &\quad {}\cdot (2^8 + 3^8)(2^{16} + 3^{16}) \\ &\quad {}\cdot (2^{32} + 3^{32})(2^{64} + 3^{64})? \end{aligned}
$$
  1. $3^{127} + 2^{127}$
  2. $3^{127} + 2^{127} + 2 \cdot 3^{63} + 3 \cdot 2^{63}$
  3. $3^{128} - 2^{128}$
  4. $3^{128} + 2^{128}$
  5. $5^{127}$