2-6*(1/2-(3))^2+ 2^3
P for Parentheses comes first in PE(MD)(AS)
So first look for the innermost parentheses.
I'll color them red:
2-6(1/2-(3))^2+2^3
There is nothing to do in that, so we can remove them, since
there will be no confusion if we do:
2-6*(1/2-3)^2+2^3
Now start over, look for the innermost parentheses:
I'll color them red:
2-6*(1/2-3)^2+2^3
Inside the parentheses there is a division and a subtraction.
Division comes before subtraction in PE(MD)(AS),
So we divide 1 by 2 and get .5. Now we replace 1/2 by .5
2-6*(.5-3)^2+2^3
We look for the innermost parentheses:
2-6*(.5-3)^2+2^3
The only thing to do is to subtract .5-3, getting -2.5,
so we replace .5-3 by -2.5
2-6*(-2.5)^2+2^3
Now there is nothing to do inside the only parentheses. However
we cannot remove them because the number inside them is negative.
Next comes exponents, so we do the leftmost exponent, which is (-2.5)^2
which gives us 6.25, so we replace (-2.5)^2 by 6.25
2-6*6.25+2^3
There are no parentheses so we look for an exponent. There is just one
exponent left, 2^3, which gives 8, so we replace 2^3 by 8
2-6*6.25+8
Now there are no parentheses or exponents, there is one multiplication,
so we do that. 6*6.25. That gives 37.5, so we replace 6*6.25 by 37.5
2-37.5+8
The only things left are additions and subtractions, and we do additions and
subtractions as we come to them left to right.
So we do the subtraction 2-37.5 and get -35.5 so we replace 2-37.5 by -35.5
-35.5+8
And that gives
-27.5
Edwin
