Problem:
The digits and are placed in the expression below, one digit per box. What is the maximum possible value of the expression?
Answer Choices:
A.
B.
C.
D.
E.
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 . Therefore, we should minimize this number, so we can put . Now the other term is or . Clearly, is larger, so we should use that. This gives us a final value of
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions