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The Power of Zero

This entry might be better titled, “The Power of Zero to Confuse Us.” (no, not Confucius!)

A curious reader (the best kind!) asked:

I have a math question:

8/ -m0 + n0 I cannot figure if it is 8 / 0 = 0 or 8/ -2 = -4.

Please help me figure this [...]

Exponents of the Zero Power

Someone wrote in to ask:

40 * 53 is 125. Why isn’t it 0?

On the Math.Com website, problems such as 4 to the zero power times 5 to the third power have an answer of 125 as correct. Shouldn’t the answer be zero. If not, why? Thank you!

Professor Homunculus’ response:

The [...]

Multiplication, Addition of Exponents

Which is greater, x2*y2 or x2+y2?

I am thinking about an example from a GRE (graduate record exam) book that was shown to me. I think it was "Which is greater, x2+y2 or (x+y)2?

Here is the poop on how to think about examples like that. When in doubt – substitute (if you can) for [...]