Can a Number to the Zero Power be -1?
Date: 01/25/2002 at 17:06:44 From: Cheryl Subject: A number to the zero power can be -1? Dear Dr. Math, My teacher told me that (-3^0) is equal to -1. He said that although anything to the zero power is one, in this case it is not so because the zero is INSIDE the parentheses with a negative number. Is this true? Thank you so much for your help.
Date: 01/25/2002 at 20:03:45 From: Doctor White Subject: Re: A number to the zero power can be -1? Hi Cheryl, Your teacher is correct. Let me try to explain. First, there is a difference between (-3)^0 and -3^0. Lets look at a different example. 4^3 -4^3 (-4)^3 4x4x4 - 4x4x4 (-4)x(-4)x(-4) 64 - 64 -64 In the second example the number is raised to the power, not the sign. It could have been written as: -(4^3). This is read as the opposite of 4 raised to the third power. In the third example the parenthesis is raised to the power. This is read as a negative 4 raised to the third power. Now back to our original problem: (-3)^0 is 1, but -3^0 can be written as -(3^0) which is the opposite of (3^0) which is -1. I hope this helps you to see your teacher's solution. By the way, there is no difference between (-3^0) and -3^0. They both equal -1. The different one is (-3)^0, which equals 1. Let me know if you need further assistance with this problem. - Doctor White, The Math Forum http://mathforum.org/dr.math/
Date: 01/25/2002 at 21:44:39 From: Cheryl Subject: A number to the zero power can be -1? Dear Dr. White, Thank you so much for your help! Your response was so fast and extremely clear. I am very grateful. Sincerely, Cheryl
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