Download Chapter 1 REVIEW OF THE REAL NUMBER SYSTEM 1.3

Chapter 1 REVIEW OF THE REAL NUMBER SYSTEM
1.3
Exponents, Roots, and Order of Operations
Learning Objectives
1)
2)
3)
4)
5)
Use exponents.
Identify exponents and bases.
Find square roots.
Use the order of operations.
Evaluate algebraic expressions for given values of variables.
Key Terms
Use the vocabulary terms listed below to complete each statement in exercises 1−6.
factors
exponent
exponential expression
base
square root
algebraic expression
1. A number written with an exponent is an _____________________________.
2. The __________________ is the number that is a repeated factor when written with an exponent.
3. An __________________ is a number that indicates how many times a factor is repeated.
4. A __________________________ of a number r is a number that can be multiplied by itself to obtain r.
5. A collection of numbers, variables, operation symbols, and grouping symbols is a(n) _______________.
6. Two or more numbers whose product is a third number are __________________ of that third number.
Objective 1
Use exponents.
Example
Exponential Expression
If a is a real number and n is a natural number,
𝒂 = ⏟
𝒂∙𝒂∙∙∙𝒂
𝒂
𝒂
where n is the exponent, a is the base, and 𝒂 is an exponential expression.
 Exponents are also called powers.
Write each expression using exponents.
∙
1)
2) (
∙ ∙
)(
∙
∙
)(
∙
1.
)(
)(
)(
)(
)(
)
2.
Note:
The product of an even number of negative factors is positive.
The product of an odd number of negative factors is negative.
Caution Be Sure to Identify the Base Correctly
It is important to distinguish between 𝒂 and ( 𝒂) …
𝒂 = ⏟𝟏(𝒂 ∙ 𝒂 ∙ ∙ ∙ 𝒂)
𝒂
The base is 𝑎
𝒂
( 𝒂) = ⏟
( 𝒂) ∙ ( 𝒂) ∙ ∙ ∙ ( 𝒂)
𝒂
𝒂
The base is 𝑎
Evaluate each expression.
3)
4) (
(
)
3.
)
5) (
4.
)
6) (
5.
)
Objective 2
6.
Identify exponents and bases.
Identify the exponent and the base. Do not evaluate.
7)
exponent _________
base _____________
8) (
)
exponent _________
base _____________
9)
exponent _________
base _____________
10)
exponent _________
base _____________
11)
exponent _________
base _____________
12) (
)
exponent _________
base _____________
Objective 3
Find square roots.
Find each square root. If it is not a real number, say so.
13)
√
14) √
13.
14.
15)
√
15.
16)
√
16.
17) √
17.
18) √
18.
Objective 4
Use the order of operations.
Order of Operations
1. Work separately above and below any fraction bar.
2. If grouping symbols such as parentheses ( ), square brackets [ ], or absolute value bars | | are present,
start with the innermost set and work outward.
3. Evaluate all powers, roots, and absolute values.
4. Do any multiplications or divisions in order, working from left to right.
5. Do any additions or subtractions in order, working from left to right.
Simplify each expression.
√
19)
(
20)
21)
22)
( ∙
(
)
20.
)
21.
∙
(
) (
[ (
23)
24)
)
19.
[
(
√ (
) (
)
)
(
)
]
)
)
22.
(
)(
)]
23.
24.
Objective 5
Evaluate algebraic expressions for given values of variables.
Evaluate each expression if a = –1, b = 3, and c = –5.
25)
𝑎 –
25.
26)
26.
27)
27.
Evaluate each expression if x = 25, y = –3, and z = –1.
√
28)
29)
30)
28.
29.
√
30.
31) The price per gallon of gasoline can be approximated for the years 2006 – 2008 by
substituting a given year for x in the expression
𝟏
and then evaluating. Approximate the price of a gallon of gas in the year 2007.
31.
32) Residents of a certain county can use the expression
(
)
𝟏
to determine their property taxes, where v is home value. Use the expression to
calculate the amount of property taxes to the nearest dollar that the owner of a home
with a value of $190,000 would pay. Follow the order of operations.
32.