Intermediate Algebra (11th edition)

Use the rules for exponents to simplify each expression. Write the answer with only positive

exponents. Assume that all variables represent positive real numbers.

36. 
    
    
    
    37. 
        
        
        
        38. 
            
        
        
        
        
    
    
    
    

39. 40. 41.

Simplify by first writing each radical in exponential form. Leave the answer in exponential

form. Assume that all variables represent positive real numbers.

42. 
    
    
    
    43. 
        
        
        
        44. 
            
        
        
        
        
    
    
    
    

45. 46. 47.

48. 49. 50.

51.The product rule does not apply to Why?

8.3 Simplify each radical. Assume that all variables represent positive real numbers.

52. 53. 54. 55.

56. 57. 58. 59.

60. 61. 62. 63.

64. 65. 66. 67.

Simplify each radical expression.

68. 
    
    
    
    69. 
        
        
        
        70. 
            
            
            
            71. 72.Find the unknown length in the right triangle. Simplify the answer if
                applicable.
            
            
            
            
        
        
        
        
    
    
    
    

73.Find the distance between the points and

8.4 Perform the indicated operations. Assume that all variables represent positive real

numbers.

74. 
    
    
    
    75. 
        
        
        
        76. 
            
        
        
        
        
    
    
    
    


75. 
    
    
    
    78. 
        
        
        
        79. 
            
        
        
        
        
    
    
    
    

In Exercises 80 and 81, leave answers as simplified radicals.

2254 m^3 + 5296 m^332354 + 52316 - 62432 + 24512

228 - 3250 8280 - 3245 - 227 y+ 2275 y

1 - 4, 7 2 1 10, 6 2.

26153 24 p^6232 # 245 2 x# 25 x

B

4

a^9

B^81

3

r^2

B^8

3

m^15

B^27

y^3

144

2100 y^72364 p^4 q^623108 a^8 b^523632 r^8 t^4

220 275 - 2125 23 - 108

26 # 211 25 # 2 r 236 # 235 247 # 243

3 1/4# 2 1/5.

432 x 323 5 x 4326 3 x

24 k^3 # 2 k^323 m^5 # 23 m^83243 z

2 p^5

p^2

28 s^426 r^9

a r-1/2 1 r+r3/2 2

z-^1 x-3/5

2 -^2 z-1/2x

b

y-1/3#y5/6 -^1

y

1 a1/3 24

a2/3

96 2/3

96 - 1/3

5 1/4# 5 7/4

488 CHAPTER 8 Roots, Radicals, and Root Functions

8 x

6

90 °

√108 ft 2 √27 ft

√50 ft

All

Traffic

Must Exit

Iowa

Highway 64

3 √48 ft

4 √8 ft

6 √12 ft

8 √2 ft

HAPPY BIHAPPY BIRTHDAY,RTHDAY,

ELVIS!ELVIS!

January 8January 8

HAPPY BIRTHDAY,

ELVIS!

January 8

80.Find the perimeter of a rectangular elec-

tronic billboard having sides of lengths

shown in the figure.

81.Find the perimeter of a triangular elec-

tronic highway road sign having the

dimensions shown in the figure.