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Tenth Power

Stage: 3 Short Challenge Level: Challenge Level:1

$3$ is odd and the product of two odd numbers is always odd therefore (2) is true, which means that $3^{10}$ is certainly not even, so (1) is false.

$3^{10} = \left( 3^5 \right)^2$, so it is also a perfect square, meaning (3) is also true.


This problem is taken from the UKMT Mathematical Challenges.