What are the results of the following calculations?
- (a)
- 16 - 4 * 5 + 12 / 3
- (b)
- 4 + (3^2 * 2 / 6) * (7 - 21 / 3)
- (c)
- -2 * 4^2
- (d)
- (-2*4)^2

### Solutions: (a) 0 (b) 4 (c) -32 (d) 64

Sketch:

You have to evaluate each expression according to the accepted order
of operations: Parentheses, Exponentiation, Multiplication or Division,
Addition or Subtraction.

(a) For the first expression, there are no parentheses, but there are two
different pairs of numbers with either a multiplication or a division,
so we have to evaluate these operations first. The expression is now:
16 - 20 + 4 which is 0.

(b) In this expression, there are two sets of parentheses, the insides of each
must be evaluated first. If you are lucky enough to notice that the "insides"
of the second set of parentheses evaluates as 0, since anything times zero is
zero, you would not have to evaluate the first set of parentheses to
know that you will end up adding 0 to 4, so the answer is 4.

(c) and (d) Remember to evaluate parentheses before exponentiation
to realize that these give different answers. In (c) you take the second power of 4 first, then multiply by -2. In (d), you multiply to get -8, which is
then squared.