0+0 is always 0
0-0 is always 0
0*0 is always 0
0/0 is undetermined, and can basically be any value.
0^0 is a bit fuzzy. It's often used as 1 because it makes equations work.
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0 multiplied by 0 is always equal to 0, not 1. The result of multiplying any number by 0 is always 0.
Any negative number to the power of 0 is always -1
When a number is added to its additive inverse, the result is always 0.
0
No, because no matter what you multiply with 0, your answer will always be 0.