Negative Signs in Exponents
Date: 12/2/95 at 17:26:20 From: Anonymous Subject: Evaluating negative signs How do you evaluate the following equation? Is (-2^2)^3 greater than or less than 2^5? The book I have says that it is less than but my parents and a math teacher, other than my algebra teacher, say that the answer is greater than. My book says that -2^2 should be evaluated as: the opposite of 2^2 or -4. My parents say that -2^2 is 4. Help!!!!!!
Date: 12/4/95 at 1:2:22 From: Doctor Ken Subject: Re: Evaluating negative signs Hello! The central question here seems to be whether you square the negative sign or whether you don't, right? Well, when you write -2^2, it's assumed that you _don't_ square the negative sign. So -2^2 = -(2^2). If you wanted to square the negative sign too, you'd write it as (-2)^2. So -2^2 = -4, and (-2)^2 = 4. So I must agree with your book: (-2^2)^3 = -1^3 * (2^2)^3 = -1 * 2^6 = -2^6, and that's less than 2^5. Oh, and here's another thing to remember: when people write something like a^b^c, that means a^(b^c), NOT (a^b)^c. Because if they meant (a^b)^c, they might as well have written a^bc. But they wrote a^b^c. Just wanted to make sure you knew that too. -Doctor Ken, The Geometry Forum
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