STUDY SKILLS
Your textbook is a valuable resource.You will learn more if you fully make use of the
features it offers.
General Features
NTable of ContentsFind this at the front of the text. Mark
the chapters and sections you will cover, as noted on your
course syllabus.
NAnswer SectionTab this section at the back of the book
so you can refer to it frequently when doing homework.
Answers to odd-numbered section exercises are provided.
Answers to ALL summary, chapter review, test, and cumu-
lative review exercises are given.
NGlossaryFind this feature after the answer section at the
back of the text. It provides an alphabetical list of the
key terms found in the text, with definitions and section
references.
NList of FormulasInside the back cover of the text is a
helpful list of geometric formulas, along with review
information on triangles and angles. Use these for refer-
ence throughout the course.Specific Features
NObjectivesThe objectives are listed at the beginning of
each section and again within the section as the corre-
sponding material is presented. Once you finish a sec-
tion, ask yourself if you have accomplished them.
NNow Try ExercisesThese margin exercises allow you to immediately practice the
material covered in the examples and prepare you for the exercises. Check your
results using the answers at the bottom of the page.
NPointersThese small shaded balloons provide on-the-spot warnings and reminders,
point out key steps, and give other helpful tips.
NCautionsThese provide warnings about common errors that students often make
or trouble spots to avoid.
NNotesThese provide additional explanations or emphasize important ideas.
NProblem-Solving HintsThese green boxes give helpful tips or strategies to use
when you work applications.Find an example of each of these features in your textbook.
Using Your Math Textbook
OBJECTIVES296 CHAPTER 5Exponents and PolynomialsOBJECTIVE 1the number 5 is the Use exponents.Recall from Section 1.2that in the expression
called an exponential expression.baseand 2 is the exponent,or power.The expression is
when it is 1, in general, for any quantity Although we do not usually write the exponenta,Write Using Exponents
Since 3 occurs as a factor four times, the base is in exponential form and evaluate.
exponential expression is , read “3 to the fourth power” or simply “3 to the fourth.” 3 and the exponent is 4. The3 #⎧ (^3) ⎪#⎨ (^3) ⎪# (^3) ⎩= 34 = 81
34
3 # 3 # 3 # 3
EXAMPLE 1
a^1 a.
52
52 ,
The Product Rule and Power Rules for Exponents
5.1
(^1) Use exponents.
(^2) rule for exponents.Use the product
3 Use the rule
4 Use the rule
5 Use the rule
6 Use combinations of rules.
7 Use the rules forexponents in a
geometryapplication.
AbaBm=abmm.
1 ab 2 m=ambm.
1 am 2 n=amn.
EXERCISE 1NOW TRY
Write in exponentialform and evaluate. 4 # 4 # 4
NOW TRY ANSWERS1.
- (a)^43 =81; ; 4^64 - 3 (b)- 81 ; 3; 4
NOW TRY EXERCISE 2
the exponent.Evaluate. Name the base and
(a) 1 - 324 (b)- 34
CAUTIONNote the differences between Example 2(b) and 2(c).
absence of parentheses shows that the exponent 4 applies only to the base 5, not In , the parentheses show that the exponent 4 applies to the base In , the
mary,-anand 1 - a 2 nare not necessarily the same. -5.In sum-
1 - 524 -^54 - 5.Expression Base Exponent(^554)
1 - - 55424 - 5 44
The base is 5.^54
(b)
(c)
NOW TRY
1 - (^524) = 1 - (^521) - 521 - (^521) - 52 = 625
- (^54) =- 1 # (^54) =- 1 # 15 # 5 # 5 # 52 =- 625
rule, we use the definition of exponents.OBJECTIVE 2Use the product rule for exponents.To develop the product
4 factors 3 factors
factors
= 27
(^4) + 3 = 7
= 2 # 2 # 2 # 2 # 2 # 2 # 2
24 # 23 = 12 ⎩#⎪ 2 ⎨# 2 ⎪#⎧ 221 ⎩ 2 ⎪# 2 ⎨⎪#⎧ 22
4 factors of 3 NOW TRY
Evaluate. Name the base and the exponent.Evaluating Exponential Expressions
(a) 54 = 5 # 5 # 5 # 5 = 625
EXAMPLE 2
ExpressionBaseExponent Example
ann
1 - a 2 n -a 1 - - 3322 = 1 - (^321) - 32 = 9 - an (^2) =- 13 # 32 =- 9
⎩⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎧
xx Preface
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