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 •Answered• Why is it 1? From:  "Rebel" how is it that 0 to the power of 2 or to the power of any number equals 1????? TB simply sent us this website:  check here David K sent us an explanation:  Actually, you got it backwards! The number ZERO to any power is ZERO (because 0 multiplied by anything is ZERO), but any number to the power of zero is one. Then you may ask, what's zero to the power of zero then? It seems like a paradox. One way to think about this is to look at the following relationships: x^1 = x^2 / x = x^(2-1)= x x^0 = x^1 / x^1 = x^(1-1) = 1 Now if you substitute "0" in place of "x" in the 2nd equation, you have a problem because you end up with "0" in the denominator, and we all know that is an "undefined" value. I think 0^0 is undefined, yet my calculator says it's "1". Go figure! MyHeadHurts replied with this:  Not strictly true, I'm afraid. 0 to the power anything but 0 equals 0, and 0 to the power 0 equals (I think) 1, as does anything else to the power 0 (definitely). As to why this is, my math teacher told me once but I cant remember for the life of me... pavolka sang to us this answer:  Simple. One is the loneliest number that you'll ever do. Keith helped out with this:  Actually, 0 to the power of anything is undefined (like dividing by zero - any attempt at a definition leads to a contradiction). On the other hand, any number (except 0) to the power of 0 is 1. Any number (except 0) to the power of 1 is the number. So 10^1 is 10 and 10^0 is 1. C.H.U.D. faithfully replied with this:  It's not. Zero to any power is zero, not one. Curt responded with this:  it is simply a mathematical term in which any number raised to the power of zero, except zero, equals one. It is a mathematical rule that applies to make sense so just deal with it. Mr. Obvious stated this:  0 to the power of 2 does not equal 1. It equals 0. Pull up your computer's calculator and try it. Paul concluded with this:  Zero to any power does not equal one, rather it is the other way around. Any number raised to the power of zero equals one. A number raised to the power of 2 is that number multiplied by itself twice (2^2 = 2x2). The exponent indicates how many times a number is multiplied by itself (2^3 = 2x2x2). A number raised to a negative exponent indicates the inverse (2^-2 = 1/2*2). The exponent zero indicates that the number is divided by itself, which always equals 1. Click here to send this page to a friend! Back to main page

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