How is -3^2 different from (-3)^2

Answer 1

Technically, -3² = -9, where (-3)² = 9

A clear difference is shown in the following examples:

10 - 3² = 1

(10)(-3)² = 90

Answer 2

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

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

the arithmetic order of operations is

do what's in

parentheses 1st

exponents next

multiplication next

division next

addition next

subtraction last

in this example you just deal with

parentheses, exponents and multiplication

for (-3)^2, perform what's in parentheses 1st to get -3

then the exponent to get -3 times -3 = +9

for -3^2, the exponent is the 1st operation: 3x3 = 9

then multiply an implicit -1 times 9 to get -9

Answer 3

Hi, Nyah.

So, -3² = (-1)•3² = -1•3²

Since you use PEMDAS to evaluate the expression, you first use exponents and then multiplication.

so (-1)•3² = -1•3² = -1•9 = -9

For (-3)², you would evaluate it as (-3)•(-3) = 9

The parentheses make a huge difference in evaluating these numbers.

Answer 4

Hello Nyah,

You probably have heard of P.E.M.D.A.S (Parentheses-Exponents-Multiplication-Division-Addition-Subtraction). That gives us the order of operations and will help us answer your question.

For -3^2: we have subtraction (the minus sign) and an exponent (^2): According to PEMDAS, exponents come before subtraction. Therefore, you would first do 3^2, then put the minus sign for subtraction: 3^2 =9, then put minus sign ---> -3^2 = -9.

For (-3)^2: we have subtraction, exponent as before. We also have parentheses, which we didn't in the other case. According to PEMDAS, our order will be: 1) parentheses, 2) exponents, 3) subtraction

(-3)^2 = (-3) * (-3). Because you are multiplying two negative numbers, the answer will be positive.

So (-3)^2 = 9

Recap: PEMDAS explains why -3^2 = -9 while (-3)^2 = 9