Basic Mathematics for College Students

54. THE BERMUDA TRIANGLE The Bermuda
    Triangle is a triangular region in the Atlantic Ocean
    where many ships and airplanes have disappeared.
    The perimeter of the triangle is about 3,075 miles. It is
    formed by three imaginary lines. The first, 1,100 miles
    long, is from Melbourne, Florida, to Puerto Rico. The
    second, 1,000 miles long, stretches from Puerto Rico
    to Bermuda. The third extends from Bermuda back to
    Florida. Find its length.


55. What is the most difficult step of the five-step
    problem-solving strategy for you? Explain why it is.


56. Give ten words or phrases that indicate subtraction.


57. What does the word translatemean?


58. Unlike an arithmetic approach, you do nothave to
    determine whether to add, subtract, multiply, or
    divide to solve the application problems in this
    section. That decision is made for you when you solve
    the equation that mathematically describes the
    situation. Explain.

WRITING

59. Write a problem that could be represented by the
    following equation.

x  x 20  50

60. Write a problem that could be represented by the
    following equation.

2  4 x  2  x  600

Find the LCM and the GCF of the given numbers.

61. 100, 120 62. 120, 180


62. 14, 140 64. 15, 300


63. 8, 9, 49 66. 9, 16, 25


64. 66, 198, 242 68. 52, 78, 130

REVIEW

is 600 ft.

width

of a

field

plus 2 

length

of a

field

2 

is 50.

age of

son

Age of father plus

688 Chapter 8 An Introduction to Algebra

SECTION 8.6

Multiplication Rules for Exponents

Objectives

1 Identify bases and exponents.

2 Multiply exponential expressions

that have like bases.

3 Raise exponential expressions

to a power.

4 Find powers of products.

In this section, we will use the definition of exponent to develop some rules for

simplifying expressions that contain exponents.

Identify bases and exponents.

Recall that an exponentindicates repeated multiplication. It indicates how many

times the base is used as a factor. For example, represents the product of five 3’s.

Exponent 5 factors of 3

Base

In general, we have the following definition.

Natural-Number Exponents

A natural-number* exponent tells how many times its base is to be used as a

factor.

For any number and any natural number ,

factors of

*The set of natural numbers is {1, 2, 3, 4, 5,...}.

xnxxxp x

⎫⎪⎪⎬⎪⎪⎭

n x

x n

(^3) 
(^5)  3  3  3  3  3

 ⎫⎪⎪⎬⎪⎪⎭

35

1