Let a 52 deck of numbered cards be created as follows:

2 special cards: 0 and 1
25 powers of 2: 2, 4, 8, ..., 2^25
25 powers of 3: 3, 9, 27, ..., 3^25

Shuffle the deck and draw at random 3 cards. Evaluate the product of the 3 numbers, say P.

What is the probability of P=0?
What is the probability of P being a non zero integer square?
What is the probability of P being a 4-digit number?

One can't always rule out 1 as the even power of the lone power of one of the two bases, but only if that was the one chosen for one of  the base represented twice.