Intermediate Algebra (11th edition)

SECTION 1.3 Exponents, Roots, and Order of Operations 29

Complete solution available
on the Video Resources on DVD

1.3 EXERCISES

Concept Check Decide whether each statement is trueor false. If it is false, correct the

statement so that it is true.

1. 
   
   
   
   2. 
      
   
   
   
   


2. is a positive number. 4.


3. is a negative number. 6. is a positive number.
   7.The product of 10 positive factors and 10 negative factors is positive.
   8.The product of 5 positive factors and 5 negative factors is positive.
   9.In the exponential expression , is the base.


4. is positive for all positive numbers a.

Concept Check In Exercises 11 and 12, evaluate each exponential expression.

11. (a) (b)
    (c) 1 - 822 (d) - 1 - 822

82 - 82

a

- 85 - 8

1 - 627 1 - 628

 25 3 + 5 # 8 = 3 + 15 # 82

- 76 = 1 - 726 - 57 = 1 - 527

Write each expression by using exponents. See Example 1.

13. 
    
    
    
    14. 
        
        
        
        15. 
            
        
        
        
        
    
    
    
    


14. 
    
    
    
    17. 
        
        
        
        18. 
            
        
        
        
        
    
    
    
    


15. 
    
    
    
    20. 
        
    
    
    
    

Evaluate each expression. See Example 2.

21. 
    
    
    
    22. 
        
        
        
        23. 
            
            
            
            24. 
                
            
            
            
            
        
        
        
        
    
    
    
    

25. 26. 27. 28.

29. 30. 31. 32.

33. 34. 35. 36.

Find each square root. If it is not a real number, say so. See Example 3.

37. 
    
    
    
    38. 
        
        
        
        39. 
            
            
            
            40. 
                
            
            
            
            
        
        
        
        
    
    
    
    

41. 42. 43. 44.

45. 46. 47. 48.

49.Concept Check Match each square root with the appropriate value or description.

(a) (b) (c)

A. B. 12 C.Not a real number

Concept Check In Exercises 50 and 51, x represents a positive number.

50.Is positive, negative, or not a real number?

51.Is -xpositive, negative, or not a real number?

• -x

- 12

 144 - 144 -  144

- 0.49 -0.64 - 36 - 121

B

225

B 169

100

121

-  400 -  900

 81  64  169  225

- 36 - 46 - 84 - 103

1 - 523 1 - 225 1 - 228 1 - 326

a

7

10

b

3

a

4

5

b

4

a

1

6

b

4

a

1

5

b

3

42 24 0.28^3 0.91^3

z#z#z#z#z#z#z a#a#a#a#a

1 - 921 - 921 - 92 1 - 921 - 921 - 921 - 92

3

2

#^3

2

3

4

#^3

4

#^3

4

#^3

4

#^3

4

10 # 10 # 10 # 10 8 # 8 # 8

12. (a) (b)
    (c) 1 - 423 (d) - 1 - 423

43 - 43