Numbers Raised to the Negative PowerDate: 11/14/2001 at 10:35:33 From: Rosemary Subject: Numbers raised to the negative power I am in 7th grade and in Pre-Algebra. We are using numbers raised to the negative power. I know that 5^(-N) = 1/5^N. I would like to know why. My teacher said it was by definition, but I know there is a reason behind this definition. Any help would be appreciated. Thanks in advance. Rosemary Date: 11/14/2001 at 12:18:53 From: Doctor Peterson Subject: Re: Numbers raised to the negative power Hi, Rosemary. Your teacher is right that negative exponents are defined this way; but the definition is made that way for a good reason, namely so that the properties of exponents continue to be true. Look at this expression: a^b * a^-b If the property a^b * a^c = a^(b+c) still holds for negative exponents, then we find that a^b * a^-b = a^(b + -b) = a^0 Therefore, our definition has to say that a^-b = a^0 / a^b Now, how do we define a^0? Again, consider a^1 * a^0 = a^(1+0) = a^1 This means that a^0 = a^1 / a^1 = 1 Now we know that we have to define a^0 as 1, and that we have to define a^-b as 1/a^b. See the Dr. Math FAQ for more ideas in this area (mostly about a^0): n^0 (any number to zero power) http://mathforum.org/dr.math/faq/faq.number.to.0power.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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