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What 3-digit number is a perfect square and a perfect cube?

Author:
February 20th, 2023

##729=9^3=27^2##
The answer must be ##a^6## for some integer ##a## due to the properties of exponentiation. Only ##3^6 = 729## lies in the required range.
##3^6 = (3^2)^3 = 9^3##
##3^6 = (3^3)^2 = 27^2##

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