Copyright © 2011 Pearson Education, Inc.
Exponents, Roots, and Order of Operations1.51.5
1. Evaluate numbers in exponential form.2. Evaluate square roots.3. Use the order-of-operations agreement to simplify numerical expressions.4. Find the mean of a set of data.
Exponential ExpressionsExponential Expressions
52Exponent
Base
Power
Exponential Expression
Exponent: A symbol written to the upper right of a base number that indicates how many times to use the base as a factor.
Base: The number that is repeatedly multiplied.
3222222 52
Evaluate: Find the value.
Exponential ExpressionsExponential Expressions
255 squared5
5
35
= 25
5 cubed5
55
= 125
Exponential ExpressionsExponential Expressions
Base Exponent Evaluate
23 3 2 9
23 3 2 9
23 3 2 9
32 2 3 8
Opposite of
Parentheses are important!!
32 2 3 8
32 2 3 8No difference
Watch for negative numbers raised to an EVEN power!!!
Exponential ExpressionsExponential Expressions
33
5
3 3 3
5 5 5
27
125
Inverse OperationsInverse Operations
Add – Subtract
Multiply – Divide
Powers – Roots
Radicand
Radical Principal Square Root
Square RootsSquare Roots
25 5
What are the roots of 25?
5, – 5 or ±5
What is ? 25
5
Square RootsSquare Roots
16
81
64
25
4
– 9
± 8
Not a real number
Order of OperationsOrder of Operations
Parentheses = Grouping Symbols
( ) [ ]
Left to right!!!
432
Grouping Symbols???
32
Yes
No
Also roots
PEMDASPEMDAS
435
75
35
435 415
19
34 252
8516
4016
4016
24
5764
3524
11
32246412
8246412
161612
161612
12
231864100
231836
23186
266 126
18
21436
5272
1236
372
1233637
363637
04
Undefined
4912653 2
493653 2
49353 2
7359
715917
94
2716
819
32
43
32
43
128
129
121
94
2716
819
121
94
2716
93
121
93
121
39
121
41
3
4 1
1
94
2716
34
41
49
2716
34
1
13
4
34
41
1216
123
1213
1213
Arithmetic Mean or AverageArithmetic Mean or Average
To find the arithmetic mean, or average, of n numbers, divide the sum of the numbers by n.
Arithmetic mean = 1 2 ... nx x x
n
Arithmetic Mean or AverageArithmetic Mean or Average
Bruce has the following test scores in his biology class: 92, 96, 81, 89, 95, 93. Find the average of his test scores.
92 96 81 89 95 93
6
546
691
Slide 1- 19Copyright © 2011 Pearson Education, Inc.
Simplify using order of operations.
a) 18
b) 6
c) 30
d) 36
26 18 9 6
1.5
Slide 1- 20Copyright © 2011 Pearson Education, Inc.
Simplify using order of operations.
a) 18
b) 6
c) 30
d) 36
26 18 9 6
1.5
Slide 1- 21Copyright © 2011 Pearson Education, Inc.
Simplify using order of operations.
a)
b)
c)
d) undefined
3
2
2 4 2
6 30 2 4
8
300
250
361
2
11
1.5
Slide 1- 22Copyright © 2011 Pearson Education, Inc.
Simplify using order of operations.
a)
b)
c)
d) undefined
3
2
2 4 2
6 30 2 4
8
300
250
361
2
11
1.5