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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 answer actually should not [...]

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) [...]