Question

Hello

Quick question on exponents. When asked to evaluate a.) (-3)^2 and b.) -3^2 I'm inclined to answer 9 for both. But, the answers given in the book they're taken from suggest a=9 and b=-9.

Can someone explain why?

Thanks

Answer 1

the book is correct

(-3)^2 = -3 * -3 = 9

- (3)^3 = - 3* 3 = -9

when you have a 'mixture; of add/subtract and multiply/ divide the multiply/divide is performed first

Answer 2

well look at it this way:
(-3)^2=(-3)(-3) a negative times a negative is a positive (thump thump) so (-3)(-3)=9
-3^2=-(3)(3) a positive times a positive is a positive so (3)(3)=(9) and -(3)(3)=-(9)

Answer 3

the acronym BODMAS is a memory aid for the order of operations
= brackets over divide/multiply over add/subtract

Answer 4

I learned it Please Excuse My Dear Aunt Sally
You start with Parentheses, then exponents, Multiplication, Division, Addition, and Subtraction

Answer 5

(.)^2 is actually all one operator in this case; the exponent is a grouping symbol ...

Answer 6

(..)^2 means, square whatever you have inside

Answer 7

(-3)^2 means, -3 * -3 = 9

-(3)^2 mean, -(3*3) = -(9) = -9

Answer 8

Thanks for all the replies lads

What I'm unclear about is why -3^2 is not =9. I assumed squaring meant -3*-3 or multiplying the value by itself. I'm starting maths from scratch again trying to find out areas I've missed which have held me back. Order of operations was one such area but I must be missing something in exponent rules

Answer 9

-3^2 has 2 symbolds to it; and the ^2 has inherent properties that the number it is directly attached to is its main focus

Answer 10

-3^2 is the same as -(3)^2

Answer 11

an exponent is a grouping symbol, is is just as groupy as brackets

Answer 12

-3^2 reads; the opposite of the square of three.

Answer 13

ok so it doesn't imply there's a calculation to be made, its just a representation?

Answer 14

im not sure i understand your response

Answer 15

it takes practice to get a good eye to read thru the math; its like learning a new language

Answer 16

Well I suppose this makes the most sense to me -3^2 is the same as -(3)^2. If I stick to that as a rule and not ask why ;)

Answer 17

the () are imlplied, thats all

Answer 18

it like having an invisible 1 in front of a variable ... its just implied

Answer 19

Well I suppose the fact that it's implied is what I missed somewhere down the road ;)
Thanks to you and everyone else for yer time. Appreciate it

Answer 20

i notice that some people have difficulty with simplifying something like -(x - 3) - they dont get how - 3 becomes + 3 after removing the brackets It helps if you put the invisible 1 into it : that is -1(x - 3) = -1*x - 1*-3 = -x + 3

Answer 21

Got it, cheers mon