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2003 AMC 10BProblem 14P11-15~2 minPrint
Exponents, Logarithms & RadicalsNumber PropertiesSet up the equation/formula and compute; no special trick neededConsider the largest/smallest element or boundary case

Given that 38⋅52=ab,3^8\cdot5^2=a^b, where both aa and bb are positive integers, find the smallest possible value for a+ba+b .

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.