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2021 AMC 10A Question 10

AMC10 · 2021 AMC 10A

Question 10

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