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