Order of Operations question?

Question

I have an order of operations question in algebra that is stumping me.

The problem is 6[(Zsquared +3 (0+2)]
The value of Z is -4.

These are my steps so far:

6[Zsquared+3(2)]

6 [Zsquared+6]

6[-16+6]

Now I am stuck. Do I get rid of the brackets and the problem becomes 6-16+6, or do I keep the brackets and multiply using the distributive property?

Also, if you see any problems with the work I have done so far, please let me know. Thanks!

God bless!

Another Question:

-12-2squared divided by 16 becomes -1 right?

Answer 1

6[z^2+3(2)]

6[z^2+6]

2 options - distribute first, or calculate what is in the brackets:

1.) 6z^2 + 36
6(16) + 36
132

2.) 6[16 + 6]
6[22]
132

Either would work, the most correct for order of operations is to complete the calculations inside the brackets first. (keep in mind -4 squared is positive 16)

Answer 2

you always work left to right except when there are parentheses, do what is inside the parentheses first (left to right)...
Please Excuse My Dear Aunt Sally (Parentheses, Exponents, Multilcaption, Division, Addition, Subtraction)
6[(Z^2 +3 (0+2)] when Z=-4
6[(-4)^2 + 3 (2)]
6(16+6)
6(22)
132
when you have a negative multiplied by it's self it is a positive. if you has (-4)^3, it would result in it being negative.... all squares will be possitive, unless the negative is outside the parenthesis...

Answer 3

So far so good, but -4 squared is not -16. It is 16.

So you have 6(16+6) = 6(22) = 132.

Answer 4

you've done everything correctly so far as far as order of operations is concerned. now combine the things inside the brackets and multiply that by six.

you have one error that is giving you an incorrect answer, however. (-4)^2 is 16, not -16. When you multiply two negatives, the answer is positive. It may be counter-intuitive, but that's the way it is.

Good work!

Answer 5

I object to the "Please Excuse My Dear Aunt Sally".

Multiplication is NOT always done before division.
Addition is NOT always done before subtraction.

25 / 5 X 2 = 10

If you were to do Multiplication first you would get 2.5.

Multiplication and Division are done simultaneously left to right.
Addition and Subtraction are done simultaneously left to right.

But the answer is 132.

6((-4)^2+3(0+2))

6(16+3(2))

6(16+6)

6(22)

132

Answer 6

The order of operations is as follows

Please Excuse My Dear Aunt Sally always left to right. in that order as far as the brackets go you do those first.


Parentheses, Exponents, Multilcaption, Division, Addition, Subtraction

Answer 7

6[(z²+3(0+2)]
= 6[z²+3(2)]
= 6[z²+6]
= 6[(-4)²+6]
= 6[16+6]
= 6[22]
= 132

Also,
(-12-2)²/16
= (-14)²/16
= 196/16
= 12.25

Answer 8

Your next step should be this:

6[-10]

And then:

60

Hope that helps...always work out the contents of the brackets before you have them affect anything outside of the brackets.

Answer 9

-4*-4=16 not -16
16 plus 6 is 22
6 * 22 is 132 and that is your answer

Answer 10

-4 squared does not equal -16 ! it is 16. answer is 6*32