Basic Mathematics for College Students

2.4 Multiplying Integers 169

EXAMPLE (^5) Evaluate: a. b.
StrategyWhen possible, we will use the commutative and/or associative
properties of multiplication to multiply pairs of negative factors.
WHYThe product of two negative factors is positive. With this approach, we work
with fewer negative numbers, and that lessens the possibility of an error.
Solution
a.Note that this expression is the product of three (an odd number) negative
integers.
Multiply the first two negative factors to produce a
positive product.
The product is negative.
b.Note that this expression is the product of four (an even number) negative
integers.
Multiply the first two negative factors and the last
two negative factors to produce positive products.
 180 The product is positive.

3(2)(6)(5)6(30)

 40

2(4)(5) 8 (5)

2(4)(5) 3(2)(6)(5)

Self Check 5

Evaluate each expression:

a.

b.

Now TryProblems 53 and 57

2(7)(1)(2)

1(2)(5)

b. Multiply the negative factors to produce a positive
product: 9(1) 9.

c. Multiply the first two negative factors to produce

a positive product. Multiply the last two factors.

Use the rule for multiplying two integers that

have different signs.

 120

3(5)(2)(4)15(8)

 72

 9 (8)(1) 9 (8)

Example 5, part a, illustrates that a product is negative when there is an odd
number of negative factors. Example 5, part b, illustrates that a product is positive
when there is an even number of negative factors.

Multiplying an Even and an Odd Number of Negative Integers

The product of an even number of negative integers is positive.

The product of an odd number of negative integers is negative.

4 Evaluate exponential expressions that have negative bases.

Recall that exponential expressions are used to represent repeated multiplication. For
example, 2 to the third power, or 2^3 , is a shorthand way of writing. In this
expression, the exponentis 3 and the base is positive2. In the next example, we
evaluate exponential expressions with bases that are negative numbers.

2  2  2

EXAMPLE (^6) Evaluate each expression: a. b. c.
StrategyWe will write each exponential expression as a product of repeated
factors and then perform the multiplication. This requires that we identify the base
and the exponent.
WHYThe exponent tells the number of times the base is to be written as a factor.

(2)^4 (5)^3 (1)^5

Self Check 6

Evaluate each expression:

a.

b.

c.(1)^7

(4)^3

(3)^4

1

4

5

 8

120