Basic Mathematics for College Students

Exponent

is called an exponential expression.

Repeated factors Base

⎫⎪⎪⎬⎪⎪⎭ ^2

2  2  2  2  24 4



An exponent is used to indicate repeated

multiplication. It tells how many times the

baseis used as a factor.

124 Chapter 1 Whole Numbers

We can use the definition of exponent to

evaluate (find the value of) exponential

expressions.

Evaluate:

Write the base 7 as a factor 3 times.

Multiply, working left to right.

Multiply.

Evaluate:

Evaluate the exponential expressions first.

 108 Multiply.

22  33  4  27

22  33

 343

 49  7

73  7  7  7

73

Find all of the factors of each number. List them from least to

greatest.

87. 18 88. 75


88. Factor 20 using two factors.Do not use the factor 1
    in your answer.


89. Factor 54 using three factors.Do not use the factor 1
    in your answer.

Tell whether each number is a prime number, a composite

number, or neither.

91. a. 31 b. 100
    c. 1 d. 0
    e. 125 f. 47

Tell whether each number is an even or an odd number.

92. a. 171 b. 214
    c. 0 d. 1

Find the prime factorization of each number. Use exponents in

your answer, when helpful.

93. 42 94. 75


94. 220 96. 140

Write each expression using exponents.

97. 
    
    
    
    98. 
        
    
    
    
    

Evaluate each expression.

99. 
    
    
    
    100. 
         
    
    
    
    


100. 24  72 102. 22  33  52

53 112

6  6  6  6 5(5)(5)(13)(13)

REVIEW EXERCISES

SECTION 1.8 The Least Common Multiple

and the Greatest Common Factor

The multiplesof a number are the products of

that number and and so on.

The least common multiple (LCM)of two

whole numbers is the smallest common

multiple of the numbers.

The LCM of two whole numbers is the

smallestwhole number that is divisible by both

of those numbers.

1, 2, 3, 4, 5,

DEFINITIONS AND CONCEPTS EXAMPLES

Multiples of 2:

Multiples of 3:

The common multiples of 2 and 3 are:

The least common multiple of 2 and 3 is 6, which is written as:

LCM

and

6

3

 2

6

2

 3

(2, 3)6.

6, 12, 18, 24, 30, p

3, 6 , 9, 12 , 15, 18 , 21, 24 , 27, p

2, 4, 6 , 8, 10, 12 , 14, 16, 18 , 20, 22, 24 , p