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