How can you recognise square numbers by looking at its prime factors?

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Also how can yo do this with cube numbers? And the same with a cube number that is also square? Thanks.

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A number is square of the indices of its prime factorization are all even.

A number is a cube of the indices of its prime factorization are all multiple of $3$.

A number is both a cube and a square if the indices of its prime factorization are multiples of $6$.

Can you see why?