SOLUTION: I have a difficulty with my daughter's algebra book. She has been taught something about apply exponents to negative numbers I am not so sure about. specifically she was taught t

Question 157295: I have a difficulty with my daughter's algebra book. She has been taught something about apply exponents to negative numbers I am not so sure about. specifically she was taught that -8^2=-64, in effect that the formula is equivalent to -(8)^2, whereas I thought it was the equivalent to (-8)^2 and therefore would be +64. We checked her textbook and it clearly supports what she was taught, but clearly contradicts what I do in engineering. Can someone either correct me or point me to a correct resource?
Found 2 solutions by midwood_trail, gonzo:
Answer by midwood_trail(310) (Show Source): You can put this solution on YOUR website!
I understand what you are saying.
Math and physics textbooks are famous for having lots of typos.
I have a closet full of math books and I cannot begin to number how many
so-called right answers are located in the back of each book.
Anytime we square a number, the answer is POSITIVE.
I am not an engineer but consider myself good at math.
It makes perfect sense that (-8)^2 DOES NOT EQUAL -(8)^2.
Case 1:
(-8)^2 = 64
Case 2:
-(8)^2 = -(64) = -64
In case 2, we apply PEMDAS. As you know, solving exponents come BEFORE multiplication in PEMDAS.
I would say it is a textbook TYPO.
Write back.

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
either the book is wrong or your interpretation of what the book is saying is wrong.
if the book is saying that -8^2 = -64, then the book must be implying (-1)*(8)^2.
assume it was in an equation where the - sign was an operand of the equation rather than part of the number.
let's say the equation was y^5 - x^2.
what would your interpretation be then?
mine would be - (x)^2.
in this case the - sign would be an operand rather than part of the number.
i would guess the book is not teaching that (-8)^2 = -64.
could be a typo. could be just bad wording. could be your interpretation was taken out of context.
check the rest of the chapter and see if they are supporting the wrong conclusion.
books are not perfect even though they try very hard.
i would say if it's showing the number by itself, then -8^2 should imply (-8)^2 as you indicated, but if it's part of an equation, then -8^2 could definitely be interpreted as -(8)^2.

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