HMMT February, 2023

Algebra Difficulty 4.7 AIME Prove it United States

Problem:
Suppose $a$ and $b$ are positive integers such that $a^{b} = 2^{2023}$ . Compute the smallest possible value of $b^{a}$ .

Solution

Solution:
By taking $a = 2^{2023}$ and $b = 1$ , we get $b^{a} = 1$ , which is clearly the minimum.

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