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3^{10}=3\times3\times3 ...\times3 product of odd numbers \therefore odd (and not even)
\therefore (a) is not true but (b) is
3^{10} = \left( 3^5 \right)^2, so it is also a perfect square \therefore (c) is true
(because 3^{10}=\underbrace{3\times3\times...\times3}_{\text{10 times}} = \underbrace{3\times3\times...\times3}_{\text{5 times}}\times\underbrace{3\times3\times...\times3}_{\text{5 times}} = \left(3^5\right)\times\left(3^5\right))
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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