2023 AMC 8 Problem 6
Attempt Problem 6 of the 2023 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
6.
The digits and are placed in the expression below, one digit per box. What is the maximum possible value of the expression?
Answer: C
Small hint:
Avoid putting in a base
Big hint:
Use as an exponent so one factor becomes
Video solution:
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Written solution:
Note that we do not want as a base, since that would make the expression equal to
This means that must be an exponent. The number whose exponent is will automatically evaluate to
Using one of the two copies of in the factor leaves and for the other factor.
The other factor can then be or Since is larger, we use
This gives us a final value of
Thus, C is the correct answer.
Problem 6 in other years
- 1985 AMC 8
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