Beginning Algebra, 11th Edition

(f )

Apply the exponents.

Divide.

Multiply.

Add.

= 113 Subtract.

= 140 - 27

= 108 + 32 - 27

= 36 # 3 + 4 # 8 - 27

= 72 , 2 # 3 + 4 # 8 - 27

72 , 2 # 3 + 4 # 23 - 33

SECTION 1.2 Exponents, Order of Operations, and Inequality 17

NOW TRY
EXERCISE 2
Find the value of each
expression.

(a)

(b)

(c) 8 # 10 , 4 - 23 + 3 # 42

612 + 42 - 7 # 5

15 - 2 # 6

Think: 3^3 = 3 # 3 # 3

⎧⎨⎩

⎧⎨⎩ ⎧⎨⎩

Multiplications and divisions are done from left to right as they appear. Then

additions and subtractions are done from left to right as they appear. NOW TRY

OBJECTIVE 3 Use more than one grouping symbol. In an expression such as

we often use brackets, in place of one pair of parentheses.

Using Brackets and Fraction Bars as Grouping Symbols

Simplify each expression.

(a)

Add inside parentheses.

Multiply inside brackets.

Add inside brackets.

= 82 Multiply.

= 23414

= 238 + 334

= 238 + 311124

238 + 316 + 524

EXAMPLE 3

218 + 316 + 522 , 34 ,

NOW TRY
EXERCISE 3
Simplify each expression.

(a)

(b)

9114 - 42 - 2

4 + 3 # 6

73132 - 12 + 44

NOW TRY ANSWERS

2. (a) 3 (b) 1 (c) 60


3. (a) 84 (b) 4

(b) Simplify the numerator and denominator separately.

Work inside parentheses.

Multiply.

= or 7 Add and subtract. Then divide. NOW TRY

35

5

,

=

32 + 3

6 - 1

=

4182 + 3

2132 - 1

415 + 32 + 3

2132 - 1

NOTE The expression in Example 3(b)can be written as the quotient

which shows that the fraction bar “groups” the numerator and denominator separately.

3415 + 32 + 34 , 32132 - 14 ,

415 + 32 + 3

2132 - 1

OBJECTIVE 4 Know the meanings of , <, >, , and. So far, we have

used the equality symbol The symbols and are used to express an

inequality,a statement that two expressions may not be equal. The equality symbol

with a slash through it, means “is not equal to.”

7 is not equal to 8.

If two numbers are not equal, then one of the numbers must be less than the other.

The symbol represents “is less than.”

768 7 is less than 8.

6

7 Z 8

Z,

=. Z, 6 , 7 ,..., Ú

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