Exponents and Negative numbers
Date: 03/02/97 at 11:15:14 From: Anonymous Subject: Exponents and negative numbers Dear Dr. Math, In different texts about this same question, I can find two different answers. The solution to: (-3)squared = 9. But when -3 is squared (without the brackets), one source may say 9 while another source says -9. In context, the -3 squared used in sequence will always be -9; why would the exponent apply to the negative sign unless it is enclosed by a sign of grouping? In short, why wouldn't the answer to -3 squared, standing alone and without parenthesis or brackets, be -9? Thanks very much. Sincerely, Marvin E. Crim
Date: 03/09/97 at 14:53:39 From: Doctor Ken Subject: Re: exponents and negative numbers Hi Marvin - After a lengthy discussion among the Drs. Math to make sure we had our facts straight, I think we have an answer for you. If you ever see the expression -3^2 evaluated as 9, that's incorrect. The exponentiation is always done before the negation unless there are parentheses there to indicate otherwise. However, there are some contexts in which it _looks_ like texts are saying that -3^2 = 9, but a closer inspection will either reveal a subtle interpretation or a misunderstanding. For instance, what is the difference between the following statements: "If I take negative three and square it, I get nine." "If I square negative three, I get nine." "If I evaluate negative three squared, I get negative nine." "If I take the opposite of three squared, I get negative nine." All of the above statements are correct. The reason some of them end up with 9 as the answer and some end up with -9 is that some of the statements have groupings implied in their phrasing. The first two statements translate into algebraic notation as (-3)^2 = 9, the third statement translates to -3^2 = -9, and the fourth statement translates to -(3^2) = -9. So the confusion here is not really about mathematical notation, it's about how to translate English into mathematical notation. Either that, or your textbook is incorrect! I hope we've cleared up some confusion. The bottom line is that -a^b is always evaluated as -(a^b). -Doctor Ken, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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