# Exponential Notation and Order of Operations

```Goals:
Exponential Notation
and Order of
Operations
Exponent Notation and terminology:
1. Interpret exponents as multiplication
2. Apply order of operations to
simplifying algebraic expressions
Exponent operation:
For b a real number, and n a positive
integer:
b
exponent
n
bn = b . b . b . . . b (b multiplied by itself n
times)
Example:
2 4 = 2 . 2 . 2 . 2 = 16
base
Examples:
1. Evaluate or simplify:
a) 33
b) (4x)2
Exponents and like terms:
Like terms – exactly alike in their
variable part:
x2y and 3x2y are like terms;
2. Write in exponential form:
xy and 3x2y are not like terms!
6ab . 6ab . 6ab . 6ab . 6ab
1
Order of Operations:
PEMDAS
p
Parenthesis
E
Exponents
M
Multiplication
D
Division
A
S
Subtraction
Otherwise,
order that the
operations
appear in the
expression
equal in priority
Examples:
Evaluate or simplify:
1. 10 – 2 &times; 8 + 3
2. (5 + 7)2
3. 52 + 72
4. – x2
equal in priority
Examples (cont’d):
6. 45 &divide; 5 &times; 2
7. 9 &divide; 3 – 7 &times; 2 + (3 + 1)2
5. (– x)2
Property of -1:
For any real number a,
–1 . a = – a
8. [4 + (1 – 2) ] . 6
9. 5(8 –6)3 &divide; 2
Opposite of a Sum:
10. 2(x + 5) – x
For real numbers a and b,
11. 2x(7 – x) + 7x 2 – 2x
–(a + b) = – a + (– b) = – a – b
Examples: Simplify:
1. – (5a + 3b + 8)
2. – (5a + 3b – 8)
3. 7t – (6 + 2t)
4. r3 + 3r – (6r3 – r)
5. 3x – [7(x2 + x) – 1]
2
```