1982 AMC 12 Problem 3

Attempt Problem 3 of the 1982 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 1982 AMC 12 solutions, or check the answer key.

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

3.

Evaluate (xx)(xx)(x^x)^{(x^x)} at x=2.x=2.
1616
6464
256256
10241024
65,53665{,}536
Answer: C
Concepts:exponentsubstitution
Small hint:
Evaluate the inner xxx^x first
Big hint:
The same value becomes both the base and exponent
Solution:
At x=2,x=2, xx=22=4.x^x=2^2=4. Hence (xx)(xx)=44=256.(x^x)^{(x^x)}=4^4=256.
Therefore, the correct answer is C.
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