OBJECTIVES
296 CHAPTER 5 Exponents and Polynomials
OBJECTIVE 1 Use exponents.Recall from Section 1.2that in the expression
the number 5 is the baseand 2 is the exponent,or power.The expression is
called an exponential expression.Although we do not usually write the exponent
when it is 1, in general, for any quantity a,
Using ExponentsWrite in exponential form and evaluate.
Since 3 occurs as a factor four times, the base is 3 and the exponent is 4. The
exponential expression is , read “3 to the fourth power” or simply “3 to the fourth.”
⎧ ⎪⎨ ⎪⎩
3 # 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 Use the product
rule for exponents.
3 Use the rule4 Use the rule5 Use the rule6 Use combinations
of rules.
7 Use the rules for
exponents in a
geometry
application.AabB
m
=am
bm.1 ab 2 m=ambm.1 am 2 n=amn.NOW TRY
EXERCISE 1
Write in exponential
form and evaluate.
4 # 4 # 4
NOW TRY ANSWERS
- (a)81; ; 4- 3 (b)- 81 ; 3; 4
43 = 64NOW TRY
EXERCISE 2
Evaluate. Name the base and
the exponent.
(a) 1 - 324 (b) - 34
CAUTION Note the differences between Example 2(b) and 2(c).In , the
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 sum-
mary, -anand 1 - a 2 nare not necessarily the same.
1 - 524 - 5.
- 5.
- 54
Expression Base Exponent
5 4
5 4
1 - 524 - 5 4- 54
54The base is 5.(b)
(c) 1 - 524 = 1 - 521 - 521 - 521 - 52 = 625 NOW TRY
- 54 = - 1 # 54 =- 1 # 15 # 5 # 5 # 52 =- 625
OBJECTIVE 2 Use the product rule for exponents.To develop the product
rule, we use the definition of exponents.
4 factors 3 factorsfactors= 27
4 + 3 = 7= 2 # 2 # 2 # 2 # 2 # 2 # 2
24 # 23 = 12 # 2 # 2 # 2212 # 2 # 22
⎩⎪ ⎨⎪ ⎧ ⎩⎪⎨⎪⎧
4 factors of 3 NOW TRYEvaluating Exponential ExpressionsEvaluate. Name the base and the exponent.
(a) 54 = 5 # 5 # 5 # 5 = 625
EXAMPLE 2
Expression Base Exponent Example
an
1 - a 2 n -a n 1 - 322 = 1 - 321 - 32 = 9- an - 32 =- 13 # 32 =- 9
⎩⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎧
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