Ejercicio 221

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CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 221
Expresar con signo radical y exponentes positivos:
  1. x 1 2 = 1 x 1 2 = 1 x
  2. 1 a 1 2 b 2 3 = a 1 2 b 2 3 = a b 2 3
  3. 5 a 5 7 b 1 3 = 5 a 5 7 b 1 3 = 5 a 5 7 b3
  4. 3 x 1 x 1 2 =3 x 1 x 1 2 =3 x 1+ 1 2 =3 x 1 2 = 3 x 1 2 = 3 x
  5. 2 m 2 5 n 3 4 = 2 n 3 4 m 2 5 = 2 n 3 4 m 2 5
  6. 1 4 x 1 3 = 1 4 x3
  7. x 3 5 y 2 3 = x 3 5 y 2 3 = x 3 5 y 2 3
  8. 3 a 3 2 x 1 4 = 3 a 3 2 x 1 4 = 3 a 3 2 x4 = 3 a 2 .a 2 x4 = 3 a a2 x4
  9. a 1 2 4 a 2 = 1 4 a 2 a 1 2 = 1 4 a 5 2 = 1 4 a 5 = 1 4 a 2 . a 3 = 1 4a a 3
  10. x 2 3 y 3 5 z 4 7 = y 3 5 x 2 3 z 4 7 = y 3 5 x 2 3 z 4 7
  11. x 2 m 3 n 2 5 = 1 x 2 m 3 n 2 5 = 1 x 2 m 3 n 2 5
  12. ( a 1 2 ) 3 = a 3 2 = 1 a 3 2 = 1 a 3
  13. ( x 2 3 ) 2 = x 4 3 = 1 x 4 3 = 1 x 4 3 = 1 x 3 .x 3 = 1 x x3
  14. ( a b ) 3 2 = 1 ( a b ) 3 2 = 1 a 3 2 b 3 2 = b 3 2 a 3 2 = b 3 a 3 = b 2 .b a 2 .a = b b a a = b a b a
  15. ( x 1 2 ) 1 3 = x 1 6 = 1 x 1 6 = 1 x6
    Expresar con exponentes positivos:
  16. a 3 = a 3 2 = 1 a 3 2
  17. 2 x 3 y 4 =2 x 3 2 y 2 =2 x 3 2 y 2 = 2 x 3 2 y 2
  18. a 2 3 x 5 = a 2 3 x 5 2 = a 2 3 x 5 2
  19. 3 m 2 3 5 n 3 4 = 3 m 2 3 5 n 3 4 = 3 m 2 3 n 3 4 5
  20. a 3 5 b 3 4 = b 3 4 a 3 5 = 1 a 3 5 b 3 4
  21. x 2 x 1 = x 2 . x 1 2 = x 3 2
  22. 1 a 7 b 6 = 1 a 7 2 b 2 = 1 a 7 2 b 3 a 7 2 b 3
  23. 3 x 2 3 y 4 = 3 x 2 3 y 2 = 3 y 2 x 2 3
  24. m 1 n 3 3 = m 1 2 n 3 3 = 1 m 1 2 n
    Hallar el valor de:
  25. 1 6 3 2 = 1 6 3 = 1 6 2 .16 =16 16 =16( 4 ) =64
  26. 8 2 3 = 8 2 3 = ( 2 3 ) 2 3 = 2 2 =4
  27. 8 1 3 4 = 8 1 3 4 = ( 3 4 ) 3 4 = 3 3 =27
  28. 9 5 2 = 1 9 5 2 = 1 9 5 = 1 ( 3 2 ) 5 = 1 3 5 = 1 243
  29. (27 ) 2 3 = 2 7 2 3 = ( 3 3 ) 2 3 = (3 ) 2 =9
  30. (32 ) 2 5 = (32 ) 2 5 = ( 2 5 ) 2 5 = (2 ) 2 =4
  31. 4 9 3 2 = 1 4 9 3 2 = 1 4 9 3 = 1 ( 7 2 ) 3 = 1 7 3 = 1 343
  32. ( 4 9 ) 5 2 = ( 4 9 ) 5 = ( 2 2 3 2 ) 5 = 2 5 3 5 = 32 243
  33. ( 8 27 ) 1 3 = ( 27 8 ) 1 3 = 27 8 3 = ( 3 2 ) 3 3 = 3 2
  34. ( 25 36 ) 1 2 = ( 36 25 ) 1 2 = 36 25 = ( 6 5 ) 2 = 6 5
  35. ( 32 243 ) 1 5 = ( 243 32 ) 1 5 = 243 32 5 = ( 3 2 ) 5 5 = 3 2
  36. ( 27 64 ) 2 3 = ( 64 27 ) 2 3 = ( 64 27 ) 2 3 = [ ( 4 3 ) 3 ] 2 3 = ( 4 3 ) 2 = 16 9
  37. 1 9 3 = 9 3 =729
  38. ( 16 81 ) 5 4 = ( 81 16 ) 5 4 = ( 81 16 ) 5 4 = [ ( 3 2 ) 4 ] 5 4 = ( 3 2 ) 5 = 243 32
  39. ( 32 243 ) 2 5 = ( 243 32 ) 2 5 = ( 243 32 ) 2 5 = [ ( 3 2 ) 5 ] 2 5 = ( 3 2 ) 2 = 9 4
  40. (2 7 9 ) 3 2 = ( 25 9 ) 3 2 = ( 9 25 ) 3 2 = ( 9 25 ) 3 = [ ( 3 5 ) 2 ] 3 = ( 3 5 ) 3 = 27 125
  41. (5 1 16 ) 1 4 = ( 81 16 ) 1 4 = ( 16 81 ) 1 4 = ( 2 3 ) 4 4 = 2 3
  42. 8 2 3 × 4 3 2 = ( 2 3 ) 2 3 × ( 2 2 ) 3 2 = 2 2 × 2 3 = 2 5 =32
  43. 9 5 2 × 2 7 1 3 = ( 3 2 ) 5 2 × ( 3 3 ) 1 3 = 3 5 × 3 1 = 3 4 =81
  44. 24 3 1 5 × 12 8 3 7 = ( 3 5 ) 1 5 × ( 2 7 ) 3 7 = 3 1 × 2 3 = 8 3