Home Competitions AMC 10 2021a Problem 10
Which of the following is equivalent to
( 2 + 3 ) ( 2 2 + 3 2 ) ( 2 4 + 3 4 ) ( 2 8 + 3 8 ) ( 2 16 + 3 16 ) ( 2 32 + 3 32 ) ( 2 64 + 3 64 ) ? (2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})? ( 2 + 3 ) ( 2 2 + 3 2 ) ( 2 4 + 3 4 ) ( 2 8 + 3 8 ) ( 2 16 + 3 16 ) ( 2 32 + 3 32 ) ( 2 64 + 3 64 )? (A) 3 127 + 2 127 (B) 3 127 + 2 127 + 2 ⋅ 3 63 + 3 ⋅ 2 63 (C) 3 128 − 2 128 (D) 3 128 + 2 128 (E) 5 127 \textbf{(A)} ~3^{127} + 2^{127} \textbf{(B)} ~3^{127} + 2^{127} + 2 \cdot 3^{63} + 3 \cdot 2^{63} \textbf{(C)} ~3^{128}-2^{128} \textbf{(D)} ~3^{128} + 2^{128} \textbf{(E)} ~5^{127} (A) 3 127 + 2 127 (B) 3 127 + 2 127 + 2 ⋅ 3 63 + 3 ⋅ 2 63 (C) 3 128 − 2 128 (D) 3 128 + 2 128 (E) 5 127
Dataset text NuminaMath-1.5 . Quoted with source.
Show the answer
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Add a solution
Similar problems
These problems have the most words in common with this statement.
Locator amc10/2021a/p10 · Tag PNCMPNXX4G · Edit this page on GitHub · Keys: j next, k previous