Exponents and parenthesis

Question

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

andwer is -9 correct? 

Answer 1

An expression such as -x is an abbreviated form of the expression

(-1)(x).

 

So, -3² = -1(3²) = (-1)(9) = -9

 

(-3)² = (-3)(-3) = 9

 

Thus,  -3² ≠ (-3)²

Answer 2

Always follow P-E-M-D-A-S  (Please Excuse My Dear Aunt Sally) --

    Parentheses

    Exponentiation

    Multiplication, Division   -- L to R

    Addition, Subtraction   --  L to R

 

For this problem, there is a unary minus (that is, -x) for a negative number.  It should be treated as subtraction from 0 (that is, 0-x).

 

Exponentiation is performed first for:

     -3²       is like   -(3²)

 

Also, multiplication and division are performed first, but it doesn't matter in their cases:

   -3*4     is like  -(3*4)     but that's the same as   (-3)*4

  -12/4    is like   -(12/4)    but that's the same as   (-12)/4

 

Parentheses cause the unary minus (same as subtract from 0) to be performed first, so:

   (-3)²    is like (-3)*(-3)    and the result is   9          (note: which is like  +9)

Answer 3

Hey Nathan,

 

It is all depends how you write it.

 

If you write as (-3)², then it will be 9.  But if you write -(3)², then it will be -9.