Beginning Algebra, 11th Edition

SECTION 1.2 Exponents, Order of Operations, and Inequality^15

OBJECTIVES

Exponents, Order of Operations, and Inequality

1.2

1 Use exponents.

2 Use the rules for

order of operations.

3 Use more than one

grouping symbol.

4 Know the meanings

of , , , ,

and.

5 Translate word

statements to

symbols.

6 Write statements

that change the

direction of

inequality symbols.

Ú

Z 6 7 ...

OBJECTIVE 1 Use exponents. Consider the prime factored form of 81.

The factor 3 appears four times.

In algebra, repeated factors are written with an exponent, so the product

is written as and read as “3 to the fourth power.”

Exponent

4 factors of 3 Base

The number 4 is the exponent,or power,and 3 is the basein the exponential expres-

sion A natural number exponent, then, tells how many times the base is used as a

factor. A number raised to the first power is simply that number.For example,

and

Evaluating Exponential Expressions

Find the value of each exponential expression.

(a)

5 is used as a factor 2 times.

Read as “5 to the second power” or, more commonly, “5 squared.”

(b)

6 is used as a factor 3 times.

Read as “6 to the third power” or, more commonly, “6 cubed.”

(c) 2 is used as a factor 5 times.

Read as “2 to the fifth power.”

(d) is used as a factor 3 times.

(e) 1 0.3 22 = 0.3 1 0.3 2 =0.09 0.3 is used as a factor 2 times. NOW TRY

2

a 3

2

3

b

3

=

2

3

#^2

3

#^2

3

=

8

27

25

25 = 2 # 2 # 2 # 2 # 2 = 32

63

63 = 6 # 6 # 6 = 216

52

52 = 5 # 5 = 25

EXAMPLE 1

a

1

2

b

1

=

1

2

51 = 5.

34.

3 # 3 # 3 # 3 = 34

34

3 # 3 # 3 # 3

81 = 3 # 3 # 3 # 3

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NOW TRY
EXERCISE 1
Find the value of each
exponential expression.

(a) (b) a

4

5

b

3

62

NOW TRY ANSWERS

1. (a) 36 (b) 12564

CAUTION Squaring, or raising a number to the second power, is NOT the

same as doubling the number.For example,

means not

Thus not6. Similarly, cubing, or raising a number to the third power, does

notmean tripling the number.

OBJECTIVE 2 Use the rules for order of operations.When a problem in-

volves more than one operation, we often use grouping symbols,such as parentheses

, to indicate the order in which the operations should be performed.

Consider the expression To show that the multiplication should be

performed before the addition, we use parentheses to group

5 + 12 # 32 equals 5 + 6, or 11.

2 #3.

5 + 2 #3.

1 2

32 =9,

32 3 #3, 2 #3.