198 Chapter 2 The Integers
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.positive
Four negative factors:
negative
Five negative factors: 2(4)(3)(1)(5) 1205(1)(6)(2) 60
Even and odd powers of a negative integer
When a negative integer is raised to an even power,
the result is positive.
When a negative integer is raised to an odd power,
the result is negative.Evaluate: The exponent is even.
Multiply pairs of integers.
The answer is positive.
Evaluate: The exponent is odd.
8 The answer is negative.(2)^3 (2)(2)(2)
81
9(9)
(3)^4 (3)(3)(3)(3)
Although the exponential expressions and
look similar, they are not the same. The bases
are different.62
(6)^2 Evaluate: and36 36
(6)^2 (6)(6) 62 (66)
Since there are no parentheses around
6, the base is 6. The exponent is 2.Because of the parentheses, the
base is 6. The exponent is 2.(6)^2 62
Application problems that involve repeated
addition are often more easily solved using
multiplication.CHEMISTRY A chemical compound that is normally stored at 0°F
had its temperature lowered 8°F each hour for 6 hours. What signed
number represents the change in temperature of the compound
after 6 hours?
Multiply the change in temperature each
hour by the number of hours.
The change in temperature of the compound is 48°F.8 6 48
Multiply.
- Find the product of and the opposite of 30.
- Find the product of the opposite of 16 and the
opposite of 3. - DEFICITS A state treasurer’s prediction of a tax
shortfall was two times worse than the actual deficit
of $130 million. The governor’s prediction of the
same shortfall was even worse—three times the
amount of the actual deficit. Complete the labeling
of the vertical axis of the graph in the next column
to show the two incorrect predictions.
15
(3)(4)(2)(5) (1)(10)(10)(1)
(6)(2)(3) 4(3)(3)
4,000(17,000) 100,000(300)
1 25 (6)(34)
23(14) 5(5)
7(2) (8)(47)
REVIEW EXERCISES–130
?
?Tax ShortfallActual
DeficitState
Treasurer GovernorPredictionsMillions of dollars- MINING An elevator is used to lower coal miners
from the ground level entrance to various depths in
the mine. The elevator stops every 45 vertical feet to
let off miners. At what depth do the miners work
who get off the elevator at the 12th stop?
Evaluate each expression.
- When is evaluated, will the result be positive
or negative? - Explain the difference between and and
then evaluate each expression.
92 (9)^2
(17)^9
(8)^4 (4)^4
(5)^3 (2)^5