Order of Operations
Chapter 1, Section 4
- Exponents
- An exponential expression is bn.
- b is called the base and n is called the exponent.
- bn means multiply b by itself n times.
-
- Roots and Radicals
- A radical expression is
 .
-
 is the radical sign,
a is the radicand, and
m is the index.
-
 means the square root of a.
- The principal (or positive) square root of the number 'a' is written and is equal to the positive number that when multiplied by itself gives 'a'.
-
 means the cube root of a.
- means the mth root of a.
-
 if
 .
- Order of Operations
- These are general steps.
- Sometimes the steps must be applied to each term, as in the example in the table below,
and then applied to the whole expression.
- Example used in table: evaluate (-5[3 - 6] - 7)2 - (7 - 13) - 34
-
| Steps
|
Example
|
Remove grouping symbols: (), {}, [].
Work from innermost out.
|
(-5[-3] - 7)2 - (-6) - 34
(15 - 7)2 + 6 - 34
82 + 6 - 34
|
| Evaluate all terms containing exponents and roots.
|
64 + 6 - 81
|
| Evaluate all multiplictions and/or divisions in the
order they occur, working left to right.
|
Already did this step inside previous terms.
|
| Evaluate all additions and/or subtractions in the
order they occur, working left to right.
|
70 - 81
-11
|
- Note how the steps were followed inside grouping symbols and then followed
on the whole expression.
- Evaluating Expressions for a Specific Variable Value
- This amounts to "plugging it in."
- Example: evaluate 10(x - 3)3 - (7 - x2) at x = -5.
-
| Plug "-5" in for each "x" in the expression
|
10(-5 - 3)2 - (7 - (-5)2)
|
| Evaluate using "order of operations" steps
|
10(-8)2 - (7 - 25)
10(64) - (-18)
640 + 18
658
|
|
