Order of Operations
Chapter 1, Section 4
 Exponents
 An exponential expression is b^{n}.
 b is called the base and n is called the exponent.
 b^{n} 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 m^{th} 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)  3^{4}

Steps

Example

Remove grouping symbols: (), {}, [].
Work from innermost out.

(5[3]  7)^{2}  (6)  3^{4}
(15  7)^{2} + 6  3^{4}
8^{2} + 6  3^{4}

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  x^{2}) 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

