SOLUTION: simplify: -9(-6+2)-7{3+2(8+6)} mike

simplify: -9(-6+2)-7{3+2(8+6)}

Remember PE(MD)(AS)

1. P.     P is for "parentheses", but that includes all grouping symbols,
          parentheses, brackets and braces.  Complete all operations inside
          the innermost pair of grouping symbols first. (While working 
          inside a pair of grouping symbols, follow the order of operations 
          in the following steps)

2. E.     Complete all exponents 

3. (MD).  Complete all multiplications or divisions as you come to
          them left to right.  Neither multiplication nor division 
          has any priority over the other, except "left before right". 

4. (AS).  Complete all additions or subtractions as you come to
          them left to right.  Neither addition nor subtraction 
          has any priority over the other, except "left before right".    


-9(-6+2)-7{3+2(8+6)}

Look for the first set of grouping symbols going left to right.
I will color them red:

-9(-6+2)-7{3+2(8+6)}

We do what's inside.  The only operation is addition -6+2, so we
replace -6+2 by its result which is -4.

-9(-4)-7{3+2(8+6)}

Now there are no operations left to do inside the ( ), so we look 
for the next pair of grouping symbols going left to right, which I
will color red.

-9(-4)-7{3+2(8+6)}

These are the braces { }.  Now while working inside these braces we
start over with the order of operations.  We look for a pair of grouping 
symbols within this pair of grouping symbols.  I will color these blue.

-9(-4)-7{3+2(8+6)}

So we do what's inside the blue ( ) first. The only operation is the
addition 8+6, so we replace 8+6 by its result which is 14.

-9(-4)-7{3+2(14)}

Now there are no operations left to do inside the ( ), and there are
no more grouping symbols inside the { }, so we look for exponents within
the { }.  There are none, so we look for multiplications or divisions.
We find the multiplication 2(14). So we replace 2(14) by its result, 28

-9(-4)-7{3+28}

Now the only operation within the { } is the addition 3+28, so we
replace 3+28 by 31

-9(-4)-7{31}

Now there are no operations left in either pair of grouping symbols.

There are no exponents, so we look for multiplications and divisions
going left to right. The first one we see is -9(-4), so we replace 
-9(-4) by the result 36.

36-7{31}

There are no grouping symbols with any operations within them. There are
no exponents, so we again look for multiplications going left to right.
We find the multiplication 7{31} and replace it by its result 217.

36-217

Then finally, with only one operation left, the subtraction 36-217, we get
as our final answer

-181

Edwin