vessel 1 said:
This question is about the order of operation. (9-11)[(-10)^2*2+6(-5)^2-10^3+3*5]
The rules for the order of operation are very clear:
Parentheses (or other grouping symbols)
Exponents
Multiplication and division....IN ORDER, from left to right
Addition and subtraction.....IN ORDER, from left to right
Let me get you started on your problem. You have two sets of grouping symbols with operations inside...the parentheses at the beginning, and the square brackets.
And I have a very STRONG conviction that you should do only ONE STEP at a time, and write down the results of every step before proceeding to the next step.
So....original problem:
(9-11)[(-10)^2*2+6(-5)^2-10^3+3*5]
Do the operation inside the parentheses. 9 - 11 is the same thing as 9 + (-11), or -2. Now we have
-2 [ (-10)[sup:3jd53ug5]2[/sup:3jd53ug5]*2 + 6(-5)[sup:3jd53ug5]2[/sup:3jd53ug5] - 10[sup:3jd53ug5]3[/sup:3jd53ug5] + 3*5]
Now, we still have a grouping symbol (the square brackets) with "things to do" inside. Inside the square brackets, there are no other grouping symbols with operations inside, but there ARE exponents, so that's what we do next. Evaluate each power inside the square brackets.
(-10)[sup:3jd53ug5]2[/sup:3jd53ug5] is (-10)*(-10), or 100. (-5)[sup:3jd53ug5]2[/sup:3jd53ug5] is (-5)(-5), or 25. 10[sup:3jd53ug5]3[/sup:3jd53ug5] is (10)(10)(10), or 1000. So, we now have
-2[ 100*2 + 6(25) - 1000 + 3*5]
Ok...all of the exponents are taken care of. Next, we do multiplications and divisions in order from left to right. There ARE some multiplications inside the square brackets, which is where we are currently working. Tackle those from left to right:
-2[200 + 150 - 1000 + 15]
We still haven't finished the operations inside the square brackets...do the additions and subtractions in order from left to right. When ALL of the operations inside the square brackets are finished, you'll have one LAST thing to do....multiply by the -2 which is in front of the square brackets.
