Ejercicio 228

CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 228
Desarrollar:
  1. ( a 1 2 + b 1 2 ) 2 = ( a 1 2 ) 2 +2 a 1 2 b 1 2 + ( b 1 2 ) 2 =a+2 a 1 2 b 1 2 +b
  2. ( x 3 4 y 1 3 ) 2 = ( x 3 ) 2 2 x 3 4 y 1 3 + ( y 1 3 ) 2 = x 3 2 2 x 3 4 y 1 3 + y 2 3
  3. ( m 1 2 +2m ) 2 = ( m 1 2 ) 2 +2.2 m 1 2 +1 + (2m ) 2 = m 1 +4 m 1 2 +4 m 2
  4. ( a 2 b 3 a 3 b 2 ) 2 = ( a 2 b 3 ) 2 2 a 2+3 b 32 + ( a 3 b 2 ) 2 = a 4 b 6 2ab+ a 6 b 4
  5. ( a 1 3 b 3 4 ) 2 = ( a 1 ) 2 2.3 a 1 b 3 4 + (3 b 3 ) 2 = a 2 6 a 1 b 3 4 +9 b 3 2
  6. ( a 2 + b ) 2 = ( a 2 ) 2 +2 a 2 b + (b ) 2 = a 4 +2 a 2 b +b
  7. ( x 3 4 y 1 2 ) 2 = ( x 3 ) 2 2 x 3 4 y 1 2 + ( y 1 2 ) 2 = x 3 2 x 3 4 y 1 2 + y 1
  8. ( m 2 n 1 4 m 1 2 n 1 ) 2 = ( m 2 n 1 4 ) 2 m 2+ 1 2 n 1 4 1 + ( m 1 2 n 1 ) 2 = m 4 n 1 2 m 3 2 n 3 4 +m n 2
  9. ( a 1 3 + b 1 3 ) 3 = ( a 1 3 ) 3 +3 ( a 1 3 ) 2 b 1 3 +3 a 1 3 ( b 1 3 ) 2 + ( b 1 3 ) 3 =a+3 a 2 3 b 1 3 +3 a 1 3 b 2 3 +b
  10. ( x 2 3 3 y 1 ) 3 = ( x 2 3 ) 3 3 ( x 2 3 ) 2 (3 y 1 ) +3 x 2 3 (3 y 1 ) 2 (3 y 1 ) 3 = x 2 9 x 4 3 y 1 +3 x 2 3 .9 y 2 3 3 y 3 = x 2 9 x 4 3 y 1 +27 x 2 3 y 2 27 y 3
  11. ( m 2 3 +4 n 3 2 ) 3 = ( m 2 3 ) 3 +3 ( m 2 3 ) 2 (4 n 3 2 ) +3 m 2 3 (4 n 3 2 ) 2 + (4 n 3 2 ) 3 = m 2 +12 m 4 3 n 3 2 +3 m 2 3 4 2 n 3 + 4 3 n 9 2 = m 2 +12 m 4 3 n 3 2 +48 m 2 3 n 3 +64 n 9 2
  12. (2 a 4 3 b 1 2 ) 3 = (2 a 4 ) 3 3 (2 a 4 ) 2 (3 b 1 2 ) +3(2 a 4 ) (3 b 1 2 ) 2 (3 b 1 2 ) 3 = 2 3 a 12 3 2 . 2 2 a 8 b 1 2 + 3 3 .2 a 4 b 1 3 3 b 3 2 =8 a 12 36 a 8 b 1 2 +54 a 4 b 1 27 b 3 2
  13. ( x y3 ) 3 = ( x 1 2 ) 3 3 ( x 1 2 ) 2 y 1 3 +3 x 1 2 ( y 1 3 ) 2 ( y 1 3 ) 3 = x 3 2 3x y 1 3 +3 x 1 2 y 2 3 y
  14. ( a 1 2 + b 2 3 ) 4 = ( a 1 2 ) 4 +4 ( a 1 2 ) 3 ( b 2 3 ) +6 ( a 1 2 ) 2 ( b 2 3 ) 2 +4( a 1 2 ) ( b 2 3 ) 3 + ( b 2 3 ) 4 = a 2 +4 a 3 2 b 2 3 +6a b 4 3 +4 a 1 2 b 2 + b 8 3
  15. ( x 2 y 1 3 ) 4 = ( x 2 ) 4 4 ( x 2 ) 3 ( y 1 3 ) +6 ( x 2 ) 2 ( y 1 3 ) 2 4( x 2 ) ( y 1 3 ) 3 + ( y 1 3 ) 4 = x 8 4 x 6 y 1 3 +6 x 4 y 2 3 4 x 2 y 1 + y 4 3
  16. ( x 1 3 + y 3 4 ) 5 = ( x 1 3 ) 5 +5 ( x 1 3 ) 4 ( y 3 4 ) +10 ( x 1 3 ) 3 ( y 3 4 ) 2 +10 ( x 1 3 ) 2 ( y 3 4 ) 3 +5( x 1 3 ) ( y 3 4 ) 4 + ( y 3 4 ) 5 = x 5 3 +5 x 4 3 y 3 4 +10x y 3 2 +10 x 2 3 y 9 4 +5 x 1 3 y 3 + y 15 4
  17. ( m n3 ) 5 = ( m 1 2 ) 5 5 ( m 1 2 ) 4 ( n 1 3 ) +10 ( m 1 2 ) 3 ( n 1 3 ) 2 10 ( m 1 2 ) 2 ( n 1 3 ) 3 +5( m 1 2 ) ( n 1 3 ) 4 ( n 1 3 ) 5 = m 5 2 5 m 2 n 1 3 +10 m 3 2 n 2 3 10mn+5 m 1 2 n 4 3 n 5 3
  18. ( a 2 2 m ) 6 = ( a 2 ) 6 6 ( a 2 ) 5 (2 m 1 2 ) +15 ( a 2 ) 4 (2 m 1 2 ) 2 20 ( a 2 ) 3 (2 m 1 2 ) 3 +15 ( a 2 ) 2 (2 m 1 2 ) 4 6( a 2 ) (2 m 1 2 ) 5 + (2 m 1 2 ) 6 = a 12 12 a 10 m 1 2 +15. 2 2 a 8 m20. 2 3 a 6 m 3 2 +15. 2 4 a 4 m 2 6. 2 5 a 2 m 5 2 + 2 6 m 3 = a 12 12 a 10 m 1 2 +60 a 8 m160 a 6 m 3 2 +240 a 4 m 2 192 a 2 m 5 2 +64 m 3
  19. ( x 3 + y4 ) 5 = ( x 3 ) 5 +5 ( x 3 ) 4 ( y 1 4 ) +10 ( x 3 ) 3 ( y 1 4 ) 2 +10 ( x 3 ) 2 ( y 1 4 ) 3 +5( x 3 ) ( y 1 4 ) 4 + ( y 1 4 ) 5 = x 15 +5 x 12 y 1 4 +10 x 9 y 1 2 +10 x 6 y 3 4 +5 x 3 y+ y 5 4
  20. ( a 2 +3 a 1 +2 ) 2 = ( a 2 ) 2 + (3 a 1 ) 2 + 2 2 +2( a 2 ) (3 a 1 ) +2( a 2 ) ( 2 ) +2(3 a 1 ) ( 2 ) = a 4 +9 a 2 +4+6 a 3 +4 a 2 +12 a 1
  21. ( x 1 2 x 1 4 +2 x 1 4 ) 2 = ( x 1 2 ) 2 + ( x 1 4 ) 2 + (2 x 1 4 ) 2 +2( x 1 2 ) ( x 1 4 ) +2( x 1 2 ) (2 x 1 4 ) +2( x 1 4 ) (2 x 1 4 ) =x+ x 1 2 + 2 2 x 1 2 2 x 1 2 + 1 4 + 2 2 x 1 2 1 4 2 2 x 1 4 1 4 =x+ x 1 2 +4 x 1 2 2 x 3 4 +4 x 1 4 4
  22. ( a 1 2 +3+ a 1 2 ) 2 = ( a 1 2 ) 2 + ( 3 ) 2 + ( a 1 2 ) 2 +2( a 1 2 ) ( 3 ) +2( a 1 2 ) ( a 1 2 ) +2( 3 ) ( a 1 2 ) = a 1 +9+a+6 a 1 2 +2 a 1 2 + 1 2 +6 a 1 2 = a 1 +9+a+6 a 1 2 +2+6 a 1 2 = a 1 +6 a 1 2 +11+a+6 a 1 2
  23. (m+2 m 3 4 3 m 1 2 ) 2 = m 2 + (2 m 3 4 ) 2 + (3 m 1 2 ) 2 +2m(2 m 3 4 ) +2m(3 m 1 2 ) +2(2 m 3 4 ) (3 m 1 2 ) = m 2 + 2 2 m 3 2 + (3 ) 2 m+ 2 2 m 1+ 3 4 6 m 1+ 1 2 2 2 .3 m 3 4 + 1 2 = m 2 +4 m 3 2 +9m+4 m 7 4 6 m 3 2 12 m 5 4 = m 2 +4 m 7 4 2 m 3 2 12 m 5 4 +9m
  24. ( a 1 2 b 1 3 2+ a 1 2 b 1 3 ) 2 = ( a 1 2 b 1 3 ) 2 + (2 ) 2 + ( a 1 2 b 1 3 ) 2 +2( a 1 2 b 1 3 ) (2 ) +2( a 1 2 b 1 3 ) ( a 1 2 b 1 3 ) +2(2 ) ( a 1 2 b 1 3 ) =a b 2 3 +4+ a 1 b 2 3 4 a 1 2 b 1 3 +2 a 1 2 1 2 b 1 3 + 1 3 4 a 1 2 b 1 3 =a b 2 3 +4+ a 1 b 2 3 4 a 1 2 b 1 3 +24 a 1 2 b 1 3 = a 1 b 2 3 4 a 1 2 b 1 3 +64 a 1 2 b 1 3 +a b 2 3
  25. ( x 1 2 + x 1 4 1 ) 3 = ( x 1 2 ) 3 + ( x 1 4 ) 3 + (1 ) 3 +3 ( x 1 2 ) 2 ( x 1 4 ) +3 ( x 1 2 ) 2 (1 ) +3 ( x 1 4 ) 2 ( x 1 2 ) +3 ( x 1 4 ) 2 (1 ) +3 (1 ) 2 ( x 1 4 ) +3 (1 ) 2 ( x 1 2 ) +6(1 ) ( x 1 4 ) ( x 1 2 ) = x 3 2 + x 3 4 1+3x x 1 4 3x+3 x 1 2 x 1 2 3 x 1 2 +3 x 1 4 + 3 x 1 2 6 x 1 4 x 1 2 = x 3 2 + x 3 4 1+3 x 5 4 3x + 3x +3 x 1 4 6 x 3 4 = x 3 2 +3 x 5 4 5 x 3 4 +3 x 1 4 1
  26. ( a 2 3 2+ a 2 3 ) 3 = ( a 2 3 ) 3 + (2 ) 3 + ( a 2 3 ) 3 +3 ( a 2 3 ) 2 (2 ) +3 ( a 2 3 ) 2 ( a 2 3 ) +3 (2 ) 2 ( a 2 3 ) +3 (2 ) 2 ( a 2 3 ) +3 ( a 2 3 ) 2 ( a 2 3 ) +3 ( a 2 3 ) 2 (2 ) +6( a 2 3 ) (2 ) ( a 2 3 ) = a 2 8+ a 2 6 a 4 3 +3 a 4 3 a 2 3 +3.4 a 2 3 +3.4 a 2 3 +3 a 4 3 a 2 3 6 a 4 3 12 a 2 3 a 2 3 = a 2 8+ a 2 6 a 4 3 +3 a 2 3 +12 a 2 3 +12 a 2 3 +3 a 2 3 6 a 4 3 12 = a 2 6 a 4 3 +15 a 2 3 20+15 a 2 3 6 a 4 3 + a 2
  27. ( m 1 6 +2 m 1 3 + m 1 2 ) 3 = ( m 1 6 ) 3 + (2 m 1 3 ) 3 + ( m 1 2 ) 3 +3 ( m 1 6 ) 2 (2 m 1 3 ) +3 ( m 1 6 ) 2 ( m 1 2 ) +3 (2 m 1 3 ) 2 ( m 1 6 ) +3 (2 m 1 3 ) 2 ( m 1 2 ) +3 ( m 1 2 ) 2 ( m 1 6 ) +3 ( m 1 2 ) 2 (2 m 1 3 ) +6 m 1 6 (2 m 1 3 ) ( m 1 2 ) = m 1 2 + 2 3 m+ m 3 2 +6 m 1 3 m 1 3 +3 m 1 3 m 1 2 +3. 2 2 m 2 3 m 1 6 +3. 2 2 m 2 3 m 1 2 +3m m 1 6 +6m m 1 3 +12 m 1 6 m 1 3 m 1 2 = m 1 2 +8m+ m 3 2 +6 m 2 3 +3 m 5 6 +12 m 5 6 +12 m 7 6 +3 m 7 6 +6 m 4 3 +12m = m 3 2 +6 m 4 3 +15 m 7 6 +20m+15 m 5 6 +6 m 2 3 + m 1 2

Ejercicio 227

CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 227
Hallar el valor de:
  1. ( a 1 ) 2 = a 1( 2 ) = a 2
  2. ( a 2 b 1 ) 3 = a 2( 3 ) b 1( 3 ) = a 6 b 3
  3. ( a 3 2 ) 2 = a 3 2 (2 ) = a 3
  4. ( x 3 4 ) 3 = x 3 4 ( 3 ) = x 9 4
  5. ( m 3 4 ) 2 = m 3 (2 ) = m 3 2
  6. ( a 2 3 ) 3 = a 2 3 (3 ) = a 2
  7. ( x 4 y 1 4 ) 2 = x 4( 2 ) y 1 (2 ) = x 8 y 1 2
  8. (2 a 1 2 b 1 3 ) 2 = 2 2 a 1 2 (2 ) b 1 3 ( 2 ) =4a b 2 3
  9. ( a 3 b 1 ) 4 = a 3( 4 ) b 1( 4 ) = a 12 b 4
  10. ( x 2 3 y 1 2 ) 6 = x 2 3 () y 1 2 () = x 4 y 3
  11. (3 a 2 5 b 3 ) 5 = 3 5 a 2 5 (5 ) b 3( 5 ) =243 a 2 b 15
  12. (2 m 1 2 n 1 3 ) 3 = 2 3 m 1 2 ( 3 ) n 1 3 (3 ) =8 m 3 2 n 1

Ejercicio 225

CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 225
Dividir:
  1. a 2 entre a 2 a 2 ÷ a 2 = a 2 . a 2 = a 2+2 = a 4
  2. x 3 entre x 2 x 3 ÷ x 2 = x 3 . x 2 = x 32 = x 5
  3. m 1 2 entre m 1 4 m 1 2 ÷ m 1 4 = m 1 2 . m 1 4 = m 1 2 + 1 4 = m 3 4
  4. a 2 entre a 5 a 2 ÷ a 5 = a 2 . a 5 = a 25 = a 3
  5. x 3 entre x 7 x 3 ÷ x 7 = x 3 . x 7 = x 3+7 = x 4
  6. a 1 2 entrea a 1 2 ÷ a = a 1 2 . a 1 = a 1 2 1 = a 1 2
  7. x 2 3 entre x 1 3 x 2 3 ÷ x 1 3 = x 2 3 . x 1 3 = x 2 3 + 1 3 = x 1 3
  8. a 2 5 entre a 1 5 a 2 5 ÷ a 1 5 = a 2 5 . a 1 5 = a 2 5 + 1 5 = a 3 5
  9. m 3 4 entre m 1 2 m 3 4 ÷ m 1 2 = m 3 4 . m 1 2 = m 3 4 1 2 = m 5 4
  10. a 1 3 entrea a 1 3 ÷ a = a 1 3 . a 1 = a 1 3 1 = a 2 3
  11. 4 x 2 5 entre2 x 1 5 4 x 2 5 ÷ 2 x 1 5 =4 x 2 5 .2 x 1 5 =8 x 2 5 + 1 5 =8 x 3 5
  12. a 3 entre a 7 4 a 3 ÷ a 7 4 = a 3 . a 7 4 = a 3+ 7 4 = a 5 4
  13. x 2 y 1 entre x 3 y 2 x 2 y 1 ÷ x 3 y 2 = x 2 y 1 . x 3 y 2 = x 32 y 21 =xy
  14. a 1 2 b 1 3 entreab a 1 2 b 1 3 ÷ ab = a 1 2 b 1 3 . a 1 b 1 = a 1 2 1 b 1 3 1 = a 1 2 b 2 3
  15. a 2 b 3 entre a 1 b a 2 b 3 ÷ a 1 b = a 2 b 3 .a b 1 = a 2+1 b 31 = a 3 b 4
  16. x 1 2 y 2 3 entre x 1 2 y 1 x 1 2 y 2 3 ÷ x 1 2 y 1 = x 1 2 y 2 3 . x 1 2 y = x 1 2 + 1 2 y 2 3 +1 = y 1 3
  17. m 3 4 n 3 4 entre m 1 2 n 3 4 m 3 4 n 3 4 ÷ m 1 2 n 3 4 = m 3 4 n 3 4 . m 1 2 n 3 4 = m 3 4 + 1 2 n 3 4 3 4 = m 5 4 n 3 2
  18. 8 x 2 y 2 5 entre4x y 1 5 8 x 2 y 2 5 ÷ 4x y 1 5 =8 x 2 y 2 5 .4 x 1 y 1 5 =32 x 21 y 2 5 + 1 5 =32 x 3 y 3 5
  19. a 1 3 bentre a 1 4 b 3 a 1 3 b ÷ a 1 4 b 3 = a 1 3 b. a 1 4 b 3 = a 1 3 + 1 4 b 1+3 = a 7 12 b 4
  20. x 4 y 5 entre x 2 y 1 x 4 y 5 ÷ x 2 y 1 = x 4 y 5 . x 2 y = x 42 y 5+1 = x 6 y 4

Ejercicio 223

CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 223
Multiplicar:
  1. x 2 por x 3 x 2 . x 3 = x 23 = x 1
  2. a 2 por a 3 a 2 . a 3 = a 23 = a 5
  3. x 3 por x 3 x 3 . x 3 = x 33 = x 0 =1
  4. a 1 2 pora a 1 2 .a = a 1 2 +1 = a 3 2
  5. x 1 2 por x 1 4 x 1 2 . x 1 4 = x 1 2 + 1 4 = x 3 4
  6. a 3 4 por a 1 4 a 3 4 . a 1 4 = a 3 4 + 1 4 =a
  7. 3 m 2 5 por m 3 5 3 m 2 5 . m 3 5 =3 m 2 5 3 5 =3 m 1 5
  8. 2 a 3 4 por a 1 2 2 a 3 4 . a 1 2 =2 a 3 4 1 2 =2 a 1 4
  9. x 2 por x 1 3 x 2 . x 1 3 = x 2 1 3 = x 7 3
  10. 3 n 2 por n 2 3 3 n 2 . n 2 3 =3 n 2 2 3 =3 n 4 3
  11. 4 a 2 por a 1 2 4 a 2 . a 1 2 =4 a 2 1 2 =4 a 5 2
  12. a 1 b 2 pora b 2 a 1 b 2 .a b 2 = a 1+1 b 2+2 = =1
  13. x 3 y 1 2 por x 2 y 1 2 x 3 y 1 2 . x 2 y 1 2 = x 32 y 1 2 1 2 = x 5 = x 5
  14. 3 a 2 b 1 2 por2 a 2 b 1 2 3 a 2 b 1 2 .2 a 2 b 1 2 =6 a 22 b 1 2 1 2 =6 =6
  15. a 3 b 1 por a 2 b 2 a 3 b 1 . a 2 b 2 = a 32 b 12 =a b 3
  16. a 1 2 b 3 4 por a 1 2 b 1 4 a 1 2 b 3 4 . a 1 2 b 1 4 = a 1 2 + 1 2 b 3 4 + 1 4 =b =b
  17. m 2 3 n 1 3 por m 1 3 n 2 3 m 2 3 n 1 3 . m 1 3 n 2 3 = m 2 3 1 3 n 1 3 + 2 3 = m 1 n
  18. 2 a 1 b 3 4 pora b 2 2 a 1 b 3 4 .a b 2 =2 a 1+1 b 3 4 2 =2 b 5 4 =2 b 5 4

Ejercicio 222

CAPITULO XXX

TEORIA DE LOS EXPONENTES
Ejercicio 222
Hallar el valor numérico de:
  1. a 2 + a 1 b 1 2 + x 0 paraa =3,b=4 a 2 + a 1 b 1 2 + = 1 a 2 + b 1 2 a +1 = 1 3 2 + 4 1 2 3 +1 = 1 9 + 2 3 +1 = 1+6+9 9 = 16 9 1 7 9
  2. 3 x 1 2 + x 2 y 3 + x 0 y 1 3 parax =4,y=1 3 x 1 2 + x 2 y 3 + y 1 3 = 3 x 1 2 + x 2 y 3 + y 1 3 = 3 4 1 2 + 4 2 1 3 + 1 1 3 = 3 2 +16+1 = 3+32+2 2 = 37 2 =18 1 2
  3. 2 a 3 b+ a 4 b 1 + a 1 2 b 3 4 paraa =4,b=16 2 a 3 b+ a 4 b 1 + a 1 2 b 3 4 = 2b a 3 + b a 4 + a 1 2 b 3 4 = 2( 16 ) 4 3 + 16 4 4 + 4 1 2 1 6 3 4 = 2( 4 2 ) 4 3 + 4 2 4 + 4 1 2 4 3 2 = 1 2 + 1 16 + 1 4 = 8+1+4 16 = 13 16
  4. x 3 4 y 2 + x 1 2 y 1 3 + x 0 y 0 + x y 4 3 parax =16,y=8 x 3 4 y 2 + x 1 2 y 1 3 + x y 4 3 = x 3 4 y 2 + 1 x 1 2 y 1 3 1+ x y 4 3 =1 6 3 4 8 2 + 1 1 6 1 2 8 1 3 1+ 16 8 4 3 = ( 2 4 ) 3 4 . ( 2 3 ) 2 + 1 ( 2 4 ) 1 2 . ( 2 3 ) 1 3 1+ 2 4 ( 2 3 ) 4 3 = 2 3 . 2 6 + 1 2 2 .2 1+ 2 4 2 4 = 2 9 + 1 2 3 1 + 1 = 2 9+3 +1 2 3 = 2 12 +1 2 3 = 4096+1 8 = 4097 8 =512 1 8
  5. x 0 x 1 + y 3 y 0 +2 x 0 + x 3 4 y 2 parax =81,y=3 x 1 + y 3 +2+ x 3 4 y 2 =x+ 1 y 3 +2+ x 3 4 y 2 =81+ 1 3 3 +2+8 1 3 4 3 2 = 3 4 + 1 3 3 +2+ ( 3 4 ) 3 4 3 2 = 3 4 + 1 3 3 +2+ 3 3 . 3 2 = 3 4 + 1 3 3 +2+3 = 3 7 +1+5. 3 3 3 3 = 2187+1+135 27 = 2323 27 86 1 27
  6. a 1 2 x 1 3 + a 1 2 x 1 3 + 1 a 1 4 x 1 +3 x 0 paraa =16,x=8 a 1 2 x 1 3 + a 1 2 x 1 3 + 1 a 1 4 x 1 +3 = a 1 2 x 1 3 + 1 a 1 2 x 1 3 + a 1 4 x+3 =1 6 1 2 8 1 3 + 1 1 6 1 2 8 1 3 +1 6 1 4 8+3 = ( 2 4 ) 1 2 ( 2 3 ) 1 3 + 1 ( 2 4 ) 1 2 ( 2 3 ) 1 3 + ( 2 4 ) 1 4 ( 2 3 ) +3 = 2 2 .2+ 1 2 2 .2 +2. 2 3 +3 = 2 3 + 1 2 3 + 2 4 +3 = 2 6 +1+ 2 7 +3. 2 3 2 3 = 64+1+128+24 8 = 217 8 27 1 8
  7. a 3 b 1 +3 a 1 b 2 c 3 a 2 b 1 2 c 1 + b 1 4 + c 0 paraa =3,b=16,c=2 a 2 b 1 +3 a 1 b 2 c 3 a 2 b 1 2 c 1 + b 1 4 + = b a 2 + 3 b 2 a c 3 c a 2 b 1 2 + b 1 4 +1 = 16 3 2 + 3 ( 16 ) 2 3 ( 2 ) 3 2 3 2 ( 16 ) 1 2 +1 6 1 4 +1 = 2 4 3 2 + ( 2 4 ) 2 2 3 2 3 2 ( 2 4 ) 1 2 + ( 2 4 ) 1 4 +1 = 2 4 3 2 + 2 2 3 2 3 2 ( 2 2 ) +2+1 = 2 4 3 2 + 2 5 1 3 2 .2 +3 = 2 5 + 3 2 . 2 6 1+ 3 3 .2 3 2 .2 = 32+5761+54 18 = 661 18 36 13 18
  8. x 0 3 y 0 + x 2 3 y 1 5 + x 2 y 1 + y 0 parax =8,y=32 3 + x 2 3 y 1 5 + x 2 y 1 + = 1 3 + x 2 3 y 1 5 + y x 2 +1 = 1 3 + 8 2 3 3 2 1 5 + 32 8 2 +1 = 4 3 + ( 2 3 ) 2 3 ( 2 5 ) 1 5 + 2 5 ( 2 3 ) 2 = 4 3 + 2 2 2+ 2 5 2 6 = 4 3 +2+ 1 2 = 8+12+3 6 = 23 6 3 5 6
  9. a 1 3 1 b 4 5 + a 0 b a3 b 2 5 1 a 2 3 paraa =27,b=243 a 1 3 1 b 4 5 + a 0 b a3 b 2 5 1 a 2 3 = 1 a 1 3 b 4 5 +b a3 b 2 5 a 2 3 = 1 2 7 1 3 24 3 4 5 +243 273 24 3 2 5 2 7 2 3 = 1 ( 3 3 ) 1 3 ( 3 5 ) 4 5 + 3 5 3 3 3 . ( 3 5 ) 2 5 ( 3 3 ) 2 3 = 1 3 3 4 + 3 5 3. 3 2 3 2 = 1 3 5 + 3 6 3 4 3 3 3 = 379 3 126 1 3

Ejercicio 221

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