Ejercicios de potenciación de fracciones

Operaciones con Fracciones

1. \( \left( \frac{a^{2}}{b^{3}} \right) \cdot \left( \frac{a^{-7}}{b^{1}} \right) \) Resp: \( \frac{1}{a^{5} \cdot b^{4}} \).
2. \( \left( \frac{a^{-9}}{b^{3}} \right) \cdot \left( \frac{b^{-3}}{a^{-5}} \right) \) Resp: \( \frac{1}{a^{4} \cdot b^{6}} \).
3. \( \left( \frac{a^{2} \cdot b^{-1}}{a^{4} \cdot b^{-2}} \right) \cdot \left( \frac{a^{8} \cdot b^{-7}}{a^{-9} \cdot b^{-7}} \right) \) Resp: \( a^{15} \cdot b \).
4. \( \left( \frac{a^{9} \cdot b^{5}}{a^{1} \cdot b^{-5}} \right) \cdot \left( \frac{a^{-4}}{b^{4}} \right)^{8} \) Resp: \( \frac{1}{a^{24} \cdot b^{22}} \).
5. \( \left( \frac{a^{5}}{b^{-7}} \right) \cdot \left( \frac{a^{-1}}{b^{2}} \right) \) Resp: \( a^{4} \cdot b^{5} \).
6. \( \left( \frac{a^{-6}}{b^{0}} \right) \cdot \left( \frac{b^{-3}}{a^{9}} \right) \) Resp: \( \frac{1}{a^{15} \cdot b^{3}} \).
7. \( \left( \frac{a^{-1} \cdot b^{8}}{a^{-7} \cdot b^{6}} \right) \cdot \left( \frac{a^{7} \cdot b^{-2}}{a^{-5} \cdot b^{-9}} \right) \) Resp: \( a^{18} \cdot b^{9} \).
8. \( \left( \frac{a^{-4} \cdot b^{3}}{a^{8} \cdot b^{2}} \right) \cdot \left( \frac{a^{7}}{b^{5}} \right)^{6} \) Resp: \( \frac{a^{30}}{b^{29}} \).
9. \( \left( \frac{a^{2}}{b^{-6}} \right) \cdot \left( \frac{a^{-9}}{b^{4}} \right) \) Resp: \( \frac{b^{2}}{a^{7}} \).
10. \( \left( \frac{a^{-6}}{b^{8}} \right) \cdot \left( \frac{b^{3}}{a^{-1}} \right) \) Resp: \( \frac{1}{a^{5} \cdot b^{5}} \).
11. \( \left( \frac{a^{-7} \cdot b^{9}}{a^{-5} \cdot b^{-5}} \right) \cdot \left( \frac{a^{-7} \cdot b^{-2}}{a^{-3} \cdot b^{5}} \right) \) Resp: \( \frac{b^{7}}{a^{6}} \).
12. \( \left( \frac{a^{2} \cdot b^{1}}{a^{-1} \cdot b^{6}} \right) \cdot \left( \frac{a^{-5}}{b^{9}} \right)^{8} \) Resp: \( \frac{1}{a^{37} \cdot b^{77}} \).
13. \( \left( \frac{a^{-3}}{b^{-3}} \right) \cdot \left( \frac{a^{6}}{b^{1}} \right) \) Resp: \( a^{3} \cdot b^{2} \).
14. \( \left( \frac{a^{6}}{b^{1}} \right) \cdot \left( \frac{b^{-9}}{a^{-4}} \right) \) Resp: \( \frac{a^{10}}{b^{10}} \).
15. \( \left( \frac{a^{-6} \cdot b^{0}}{a^{-4} \cdot b^{4}} \right) \cdot \left( \frac{a^{-9} \cdot b^{-1}}{a^{-2} \cdot b^{0}} \right) \) Resp: \( \frac{1}{a^{9} \cdot b^{5}} \).
16. \( \left( \frac{a^{-1} \cdot b^{-2}}{a^{-1} \cdot b^{4}} \right) \cdot \left( \frac{a^{-8}}{b^{-4}} \right)^{-9} \) Resp: \( \frac{a^{72}}{b^{42}} \).
17. \( \left( \frac{a^{3}}{b^{-2}} \right) \cdot \left( \frac{a^{-9}}{b^{3}} \right) \) Resp: \( \frac{1}{a^{6} \cdot b^{1}} \).
18. \( \left( \frac{a^{5}}{b^{-6}} \right) \cdot \left( \frac{b^{4}}{a^{-3}} \right) \) Resp: \( a^{8} \cdot b^{10} \).
19. \( \left( \frac{a^{4} \cdot b^{1}}{a^{-1} \cdot b^{-1}} \right) \cdot \left( \frac{a^{9} \cdot b^{7}}{a^{-1} \cdot b^{5}} \right) \) Resp: \( a^{15} \cdot b^{4} \).
20. \( \left( \frac{a^{7} \cdot b^{-2}}{a^{3} \cdot b^{0}} \right) \cdot \left( \frac{a^{7}}{b^{-3}} \right)^{2} \) Resp: \( a^{18} \cdot b^{4} \).
21. \( \left( \frac{a^{7}}{b^{-4}} \right) \cdot \left( \frac{a^{-5}}{b^{-1}} \right) \) Resp: \( a^{2} \cdot b^{5} \).
22. \( \left( \frac{a^{2}}{b^{-8}} \right) \cdot \left( \frac{b^{-1}}{a^{-6}} \right) \) Resp: \( a^{8} \cdot b^{7} \).
23. \( \left( \frac{a^{2} \cdot b^{-9}}{a^{-1} \cdot b^{2}} \right) \cdot \left( \frac{a^{-8} \cdot b^{7}}{a^{5} \cdot b^{0}} \right) \) Resp: \( \frac{1}{a^{10} \cdot b^{4}} \).
24. \( \left( \frac{a^{6} \cdot b^{0}}{a^{8} \cdot b^{6}} \right) \cdot \left( \frac{a^{7}}{b^{-7}} \right)^{-7} \) Resp: \( \frac{1}{a^{51} \cdot b^{55}} \).
25. \( \left( \frac{a^{-4}}{b^{-1}} \right) \cdot \left( \frac{a^{-5}}{b^{-2}} \right) \) Resp: \( \frac{b^{3}}{a^{9}} \).
26. \( \left( \frac{a^{0}}{b^{2}} \right) \cdot \left( \frac{b^{8}}{a^{-8}} \right) \) Resp: \( a^{8} \cdot b^{6} \).
27. \( \left( \frac{a^{3} \cdot b^{-2}}{a^{0} \cdot b^{-3}} \right) \cdot \left( \frac{a^{1} \cdot b^{1}}{a^{4} \cdot b^{-8}} \right) \) Resp: \( b^{10} \).
28. \( \left( \frac{a^{-8} \cdot b^{-4}}{a^{-8} \cdot b^{4}} \right) \cdot \left( \frac{a^{6}}{b^{5}} \right)^{-2} \) Resp: \( \frac{b^{2}}{a^{12}} \).
29. \( \left( \frac{a^{6}}{b^{3}} \right) \cdot \left( \frac{a^{3}}{b^{-1}} \right) \) Resp: \( \frac{a^{9}}{b^{2}} \).
30. \( \left( \frac{a^{4}}{b^{-8}} \right) \cdot \left( \frac{b^{8}}{a^{-3}} \right) \) Resp: \( a^{7} \cdot b^{16} \).
31. \( \left( \frac{a^{-7} \cdot b^{2}}{a^{-6} \cdot b^{8}} \right) \cdot \left( \frac{a^{3} \cdot b^{2}}{a^{8} \cdot b^{9}} \right) \) Resp: \( \frac{1}{a^{6} \cdot b^{13}} \).
32. \( \left( \frac{a^{1} \cdot b^{3}}{a^{7} \cdot b^{8}} \right) \cdot \left( \frac{a^{3}}{b^{0}} \right)^{-5} \) Resp: \( \frac{1}{a^{21} \cdot b^{5}} \).
33. \( \left( \frac{a^{-1}}{b^{6}} \right) \cdot \left( \frac{a^{-3}}{b^{7}} \right) \) Resp: \( \frac{1}{a^{4} \cdot b^{13}} \).
34. \( \left( \frac{a^{4}}{b^{3}} \right) \cdot \left( \frac{b^{5}}{a^{-8}} \right) \) Resp: \( a^{12} \cdot b^{2} \).
35. \( \left( \frac{a^{-5} \cdot b^{6}}{a^{-8} \cdot b^{9}} \right) \cdot \left( \frac{a^{-9} \cdot b^{1}}{a^{1} \cdot b^{4}} \right) \) Resp: \( \frac{1}{a^{7} \cdot b^{6}} \).
36. \( \left( \frac{a^{-9} \cdot b^{2}}{a^{1} \cdot b^{0}} \right) \cdot \left( \frac{a^{-9}}{b^{-1}} \right)^{4} \) Resp: \( \frac{b^{6}}{a^{46}} \).
37. \( \left( \frac{a^{-2}}{b^{8}} \right) \cdot \left( \frac{a^{6}}{b^{0}} \right) \) Resp: \( \frac{a^{4}}{b^{8}} \).
38. \( \left( \frac{a^{-3}}{b^{-2}} \right) \cdot \left( \frac{b^{-6}}{a^{0}} \right) \) Resp: \( \frac{1}{a^{3} \cdot b^{4}} \).
39. \( \left( \frac{a^{8} \cdot b^{6}}{a^{0} \cdot b^{9}} \right) \cdot \left( \frac{a^{-4} \cdot b^{7}}{a^{3} \cdot b^{-4}} \right) \) Resp: \( a^{1} \cdot b^{8} \).
40. \( \left( \frac{a^{0} \cdot b^{9}}{a^{-6} \cdot b^{2}} \right) \cdot \left( \frac{a^{-3}}{b^{-4}} \right)^{3} \) Resp: \( \frac{b^{19}}{a^{3}} \).
41. \( \left( \frac{a^{-1}}{b^{0}} \right) \cdot \left( \frac{a^{0}}{b^{6}} \right) \) Resp: \( \frac{1}{a^{1} \cdot b^{6}} \).
42. \( \left( \frac{a^{-8}}{b^{-2}} \right) \cdot \left( \frac{b^{-4}}{a^{9}} \right) \) Resp: \( \frac{1}{a^{17} \cdot b^{2}} \).
43. \( \left( \frac{a^{0} \cdot b^{-7}}{a^{4} \cdot b^{2}} \right) \cdot \left( \frac{a^{-8} \cdot b^{3}}{a^{-5} \cdot b^{9}} \right) \) Resp: \( \frac{1}{a^{7} \cdot b^{15}} \).
44. \( \left( \frac{a^{-7} \cdot b^{-3}}{a^{-9} \cdot b^{5}} \right) \cdot \left( \frac{a^{6}}{b^{-6}} \right)^{-4} \) Resp: \( \frac{1}{a^{22} \cdot b^{32}} \).
45. \( \left( \frac{a^{-6}}{b^{-1}} \right) \cdot \left( \frac{a^{-5}}{b^{-9}} \right) \) Resp: \( \frac{b^{10}}{a^{11}} \).
46. \( \left( \frac{a^{-2}}{b^{5}} \right) \cdot \left( \frac{b^{2}}{a^{-5}} \right) \) Resp: \( \frac{a^{3}}{b^{3}} \).
47. \( \left( \frac{a^{-8} \cdot b^{5}}{a^{1} \cdot b^{-6}} \right) \cdot \left( \frac{a^{-6} \cdot b^{8}}{a^{2} \cdot b^{3}} \right) \) Resp: \( \frac{b^{16}}{a^{17}} \).
48. \( \left( \frac{a^{4} \cdot b^{8}}{a^{9} \cdot b^{2}} \right) \cdot \left( \frac{a^{8}}{b^{8}} \right)^{-1} \) Resp: \( \frac{b^{14}}{a^{13}} \).
49. \( \left( \frac{a^{2}}{b^{-3}} \right) \cdot \left( \frac{a^{-9}}{b^{3}} \right) \) Resp: \( \frac{1}{a^{7}} \).
50. \( \left( \frac{a^{-4}}{b^{8}} \right) \cdot \left( \frac{b^{-4}}{a^{-2}} \right) \) Resp: \( \frac{1}{a^{2} \cdot b^{12}} \).
51. \( \left( \frac{a^{-2} \cdot b^{-3}}{a^{-3} \cdot b^{3}} \right) \cdot \left( \frac{a^{-5} \cdot b^{3}}{a^{5} \cdot b^{9}} \right) \) Resp: \( \frac{1}{a^{9} \cdot b^{12}} \).
52. \( \left( \frac{a^{-3} \cdot b^{-2}}{a^{8} \cdot b^{-3}} \right) \cdot \left( \frac{a^{9}}{b^{5}} \right)^{-5} \) Resp: \( \frac{b^{26}}{a^{56}} \).
53. \( \left( \frac{a^{8}}{b^{-5}} \right) \cdot \left( \frac{a^{-4}}{b^{4}} \right) \) Resp: \( a^{4} \cdot b^{1} \).
54. \( \left( \frac{a^{6}}{b^{-8}} \right) \cdot \left( \frac{b^{7}}{a^{1}} \right) \) Resp: \( a^{5} \cdot b^{15} \).
55. \( \left( \frac{a^{-5} \cdot b^{-9}}{a^{-8} \cdot b^{-4}} \right) \cdot \left( \frac{a^{3} \cdot b^{-6}}{a^{-6} \cdot b^{-8}} \right) \) Resp: \( \frac{a^{12}}{b^{3}} \).
56. \( \left( \frac{a^{8} \cdot b^{0}}{a^{5} \cdot b^{8}} \right) \cdot \left( \frac{a^{1}}{b^{8}} \right)^{1} \) Resp: \( \frac{a^{4}}{b^{16}} \).
57. \( \left( \frac{a^{3}}{b^{7}} \right) \cdot \left( \frac{a^{1}}{b^{-5}} \right) \) Resp: \( \frac{a^{4}}{b^{2}} \).
58. \( \left( \frac{a^{-5}}{b^{4}} \right) \cdot \left( \frac{b^{-6}}{a^{2}} \right) \) Resp: \( \frac{1}{a^{7} \cdot b^{10}} \).
59. \( \left( \frac{a^{-1} \cdot b^{-2}}{a^{-9} \cdot b^{2}} \right) \cdot \left( \frac{a^{-3} \cdot b^{2}}{a^{-8} \cdot b^{-7}} \right) \) Resp: \( a^{13} \cdot b^{5} \).
60. \( \left( \frac{a^{3} \cdot b^{9}}{a^{-1} \cdot b^{-4}} \right) \cdot \left( \frac{a^{2}}{b^{-1}} \right)^{6} \) Resp: \( a^{16} \cdot b^{19} \).
61. \( \left( \frac{a^{6}}{b^{-6}} \right) \cdot \left( \frac{a^{-7}}{b^{-4}} \right) \) Resp: \( \frac{b^{10}}{a^{1}} \).
62. \( \left( \frac{a^{5}}{b^{-2}} \right) \cdot \left( \frac{b^{-4}}{a^{-6}} \right) \) Resp: \( \frac{a^{11}}{b^{2}} \).
63. \( \left( \frac{a^{1} \cdot b^{-4}}{a^{3} \cdot b^{8}} \right) \cdot \left( \frac{a^{2} \cdot b^{-1}}{a^{4} \cdot b^{-8}} \right) \) Resp: \( \frac{1}{a^{4} \cdot b^{5}} \).
64. \( \left( \frac{a^{-1} \cdot b^{-3}}{a^{6} \cdot b^{3}} \right) \cdot \left( \frac{a^{-8}}{b^{9}} \right)^{-9} \) Resp: \( a^{65} \cdot b^{75} \).
65. \( \left( \frac{a^{3}}{b^{-4}} \right) \cdot \left( \frac{a^{0}}{b^{-4}} \right) \) Resp: \( a^{3} \cdot b^{8} \).
66. \( \left( \frac{a^{1}}{b^{6}} \right) \cdot \left( \frac{b^{-1}}{a^{2}} \right) \) Resp: \( \frac{1}{a^{1} \cdot b^{7}} \).
67. \( \left( \frac{a^{0} \cdot b^{-1}}{a^{-4} \cdot b^{-2}} \right) \cdot \left( \frac{a^{8} \cdot b^{-2}}{a^{-3} \cdot b^{4}} \right) \) Resp: \( \frac{a^{15}}{b^{5}} \).
68. \( \left( \frac{a^{-7} \cdot b^{-9}}{a^{-4} \cdot b^{-5}} \right) \cdot \left( \frac{a^{8}}{b^{6}} \right)^{4} \) Resp: \( \frac{a^{29}}{b^{28}} \).
69. \( \left( \frac{a^{-3}}{b^{9}} \right) \cdot \left( \frac{a^{-9}}{b^{-8}} \right) \) Resp: \( \frac{1}{a^{12} \cdot b^{1}} \).
70. \( \left( \frac{a^{8}}{b^{-9}} \right) \cdot \left( \frac{b^{2}}{a^{8}} \right) \) Resp: \( b^{11} \).
71. \( \left( \frac{a^{8} \cdot b^{-9}}{a^{7} \cdot b^{0}} \right) \cdot \left( \frac{a^{4} \cdot b^{-6}}{a^{9} \cdot b^{-2}} \right) \) Resp: \( \frac{1}{a^{4} \cdot b^{13}} \).
72. \( \left( \frac{a^{-8} \cdot b^{-7}}{a^{-2} \cdot b^{-5}} \right) \cdot \left( \frac{a^{2}}{b^{-7}} \right)^{-4} \) Resp: \( \frac{1}{a^{14} \cdot b^{30}} \).
73. \( \left( \frac{a^{9}}{b^{9}} \right) \cdot \left( \frac{a^{6}}{b^{-2}} \right) \) Resp: \( \frac{a^{15}}{b^{7}} \).
74. \( \left( \frac{a^{-5}}{b^{-1}} \right) \cdot \left( \frac{b^{-7}}{a^{5}} \right) \) Resp: \( \frac{1}{a^{10} \cdot b^{6}} \).
75. \( \left( \frac{a^{5} \cdot b^{-7}}{a^{7} \cdot b^{-3}} \right) \cdot \left( \frac{a^{-3} \cdot b^{-3}}{a^{-1} \cdot b^{8}} \right) \) Resp: \( \frac{1}{a^{4} \cdot b^{15}} \).
76. \( \left( \frac{a^{4} \cdot b^{2}}{a^{8} \cdot b^{-5}} \right) \cdot \left( \frac{a^{-9}}{b^{3}} \right)^{-1} \) Resp: \( a^{5} \cdot b^{10} \).
77. \( \left( \frac{a^{-4}}{b^{7}} \right) \cdot \left( \frac{a^{4}}{b^{3}} \right) \) Resp: \( \frac{1}{b^{10}} \).
78. \( \left( \frac{a^{-4}}{b^{9}} \right) \cdot \left( \frac{b^{-5}}{a^{-2}} \right) \) Resp: \( \frac{1}{a^{2} \cdot b^{14}} \).
79. \( \left( \frac{a^{-2} \cdot b^{5}}{a^{7} \cdot b^{5}} \right) \cdot \left( \frac{a^{-9} \cdot b^{4}}{a^{-4} \cdot b^{-9}} \right) \) Resp: \( \frac{b^{13}}{a^{14}} \).
80. \( \left( \frac{a^{2} \cdot b^{-9}}{a^{-9} \cdot b^{3}} \right) \cdot \left( \frac{a^{8}}{b^{5}} \right)^{1} \) Resp: \( \frac{a^{19}}{b^{17}} \).
81. \( \left( \frac{a^{6}}{b^{4}} \right) \cdot \left( \frac{a^{7}}{b^{3}} \right) \) Resp: \( \frac{a^{13}}{b^{7}} \).
82. \( \left( \frac{a^{2}}{b^{-8}} \right) \cdot \left( \frac{b^{5}}{a^{3}} \right) \) Resp: \( \frac{b^{13}}{a^{1}} \).
83. \( \left( \frac{a^{2} \cdot b^{-2}}{a^{8} \cdot b^{-3}} \right) \cdot \left( \frac{a^{7} \cdot b^{0}}{a^{2} \cdot b^{-9}} \right) \) Resp: \( \frac{b^{10}}{a^{1}} \).
84. \( \left( \frac{a^{-6} \cdot b^{4}}{a^{-6} \cdot b^{-5}} \right) \cdot \left( \frac{a^{9}}{b^{7}} \right)^{8} \) Resp: \( \frac{a^{72}}{b^{47}} \).
85. \( \left( \frac{a^{6}}{b^{-4}} \right) \cdot \left( \frac{a^{-5}}{b^{-2}} \right) \) Resp: \( a^{1} \cdot b^{6} \).
86. \( \left( \frac{a^{-7}}{b^{4}} \right) \cdot \left( \frac{b^{-3}}{a^{-7}} \right) \) Resp: \( \frac{1}{b^{7}} \).
87. \( \left( \frac{a^{4} \cdot b^{-7}}{a^{-6} \cdot b^{5}} \right) \cdot \left( \frac{a^{5} \cdot b^{6}}{a^{8} \cdot b^{3}} \right) \) Resp: \( \frac{a^{7}}{b^{9}} \).
88. \( \left( \frac{a^{8} \cdot b^{-4}}{a^{1} \cdot b^{-2}} \right) \cdot \left( \frac{a^{1}}{b^{-3}} \right)^{3} \) Resp: \( a^{10} \cdot b^{7} \).
89. \( \left( \frac{a^{2}}{b^{-9}} \right) \cdot \left( \frac{a^{4}}{b^{1}} \right) \) Resp: \( a^{6} \cdot b^{8} \).
90. \( \left( \frac{a^{7}}{b^{7}} \right) \cdot \left( \frac{b^{5}}{a^{0}} \right) \) Resp: \( \frac{a^{7}}{b^{2}} \).
91. \( \left( \frac{a^{-6} \cdot b^{2}}{a^{1} \cdot b^{7}} \right) \cdot \left( \frac{a^{0} \cdot b^{-4}}{a^{-8} \cdot b^{-1}} \right) \) Resp: \( \frac{a^{1}}{b^{8}} \).
92. \( \left( \frac{a^{-5} \cdot b^{5}}{a^{0} \cdot b^{9}} \right) \cdot \left( \frac{a^{-4}}{b^{6}} \right)^{8} \) Resp: \( \frac{1}{a^{37} \cdot b^{52}} \).
93. \( \left( \frac{a^{0}}{b^{-2}} \right) \cdot \left( \frac{a^{-9}}{b^{-8}} \right) \) Resp: \( \frac{b^{10}}{a^{9}} \).
94. \( \left( \frac{a^{0}}{b^{8}} \right) \cdot \left( \frac{b^{8}}{a^{0}} \right) \) Resp: \( 1 \).
95. \( \left( \frac{a^{5} \cdot b^{-4}}{a^{3} \cdot b^{4}} \right) \cdot \left( \frac{a^{-7} \cdot b^{1}}{a^{-5} \cdot b^{8}} \right) \) Resp: \( \frac{1}{b^{15}} \).
96. \( \left( \frac{a^{-5} \cdot b^{6}}{a^{2} \cdot b^{6}} \right) \cdot \left( \frac{a^{-9}}{b^{5}} \right)^{-2} \) Resp: \( a^{11} \cdot b^{10} \).
97. \( \left( \frac{a^{-1}}{b^{9}} \right) \cdot \left( \frac{a^{-8}}{b^{-4}} \right) \) Resp: \( \frac{1}{a^{9} \cdot b^{5}} \).
98. \( \left( \frac{a^{3}}{b^{3}} \right) \cdot \left( \frac{b^{7}}{a^{1}} \right) \) Resp: \( a^{2} \cdot b^{4} \).
99. \( \left( \frac{a^{3} \cdot b^{-5}}{a^{6} \cdot b^{8}} \right) \cdot \left( \frac{a^{8} \cdot b^{-7}}{a^{-7} \cdot b^{-6}} \right) \) Resp: \( \frac{a^{12}}{b^{14}} \).
100. \( \left( \frac{a^{-1} \cdot b^{8}}{a^{-4} \cdot b^{0}} \right) \cdot \left( \frac{a^{4}}{b^{-2}} \right)^{-2} \) Resp: \( \frac{b^{4}}{a^{5}} \).