Yes you can. they will all end up back at zero.
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It is zero. No matter how many times you multiply a zero, it is always zero. 0.
The special property that zero has is that if you multiply zero by any number, you get zero.
For the same reason that you can't divide a number by zero.
Yes. Multiplying any number by zero results in zero.
Because zero multiplied by any number is always zero, but anything multiplied by infinity is infinity. Zero times infinity is being pulled both ways. Also, the definition of infinity is any number x divided by 0. When you multiply zero by infinity, the zeroes "cancel out", leaving absolutely nothing behind.