Why do we think 0! = 1?

Notice that when we go from 4! to 3! , we divide by 4.

(Because  the 4's cancel)

And when we go from 3! to 2! , we divide by 3, and etc.

We can use this pattern to see why 0! = 1.

And so by following the pattern, we determine that 0! = 1

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Note:

There are no factorials of negative numbers, and we can use the pattern to show why:

You can't divide a number by 0, therefore -1! doesn't exist, so -2! doesn't exist and so on. So you can't do the factorial of any negative number.

(Or at least there no real solutions to negative factorials)

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answer4 to the second power is 16

and 4 to the third power is 64,