1963 AMC 12 Problem 2

Attempt Problem 2 of the 1963 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1963 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

Let n=x−yx−y.n=x-y^{x-y}. Find nn when x=2x=2 and y=−2.y=-2.
−14-14
00
11
1818
256256
Answer: A
Concepts:substitutionexponentorder of operations
Small hint:
First compute the exponent x−yx-y
Big hint:
Evaluate the power before subtracting it from xx
Solution:
Here x−y=2−(−2)=4,x-y=2-(-2)=4, so n=2−(−2)4=2−16=−14.n=2-(-2)^4=2-16=-14.
Therefore, the correct answer is A.
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