Anything to the 0 PowerDate: 11/21/97 at 16:00:46 From: Jenna M Gambino Subject: N^0 Dear Dr. Math, Everyone in my 7th grade class wants to know the answer to this question: Why is anything to the 0 power 1? No one in my class knows the answer, not even my teacher. She asked me to e-mail Dr. Math and we are eagerly waiting to hear the answer. Thanks for your time, Jenna Date: 11/24/97 at 14:44:56 From: Doctor Steven Subject: Re: N^0 Look at the powers of any number, say 8: 8^1 = 8 8^2 = 64 8^3 = 512 . . . To get from 8^3 to 8^2 we have to divide by 8. And to get from 8^2 to 8^1 we have to divide by 8 again. The logical idea is to continue doing this so we get: to go from 8^1 to 8^0 we should divide by 8. So 8^0 = 8^1/8 = 8/8 = 1. This works for any nonzero number. 0^0 is undefined. We can even continue this process to create negative exponents: to go from 8^0 to 8^(-1) we divide by 8 So 8^(-1) = 8^0/8 = 1/8. Now we have this: . . . 8^3 = 512 8^2 = 64 8^1 = 8 8^0 = 1 8^(-1) = 1/8 8^(-2) = 1/64 8^(-3) = 1/512 . . . Hope this helps. For more, see the Dr. Math FAQ: http://mathforum.org/dr.math/faq/faq.number.to.0power.html -Doctor Steven, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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