What is the value of 2^1+2+3 - (2^1 + 2^2 + 2^3)?

2021 AMC 12A Spring Problem 1 — Solution

2021 AMC 12A Spring Problem 1

Below is the professionally curated solution for Problem 1 of the 2021 AMC 12A Spring, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2021 AMC 12A Spring solutions, or check the answer key.

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Concepts:exponent order of operations

Difficulty rating: 800

What is the value of $2^{1+2+3} - \left(2^1 + 2^2 + 2^3\right)?$

$0$

$50$

$52$

$54$

$57$

Solution:

The exponent in the first term is $1+2+3 = 6,$ so the first term is $2^6 = 64.$ The parenthesized sum is $2 + 4 + 8 = 14.$ Therefore the value is $64 - 14 = 50.$

Thus, the correct answer is B.

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