Ejercicio 242

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CAPITULO XXXI

R a d i c a l e s
Multiplicación de radicales de distinto índice
Ejercicio 242
Multiplicar:
  1. x × 2 x 2 3 x = x 3 6 2 x 2 3 = (2 x 2 ) 2 6 = 4 x 4 6 x × 2 x 2 3 = x 3 6 × 4 x 4 6 = 4 x 7 6 = 4 x 6 x 6 =x 4x 6
  2. 3 2ab × 4 8 a 3 4 3 2ab =3 (2ab ) 2 4 =3 2 2 a 2 b 2 4 3 2ab × 4 8 a 3 4 =3 2 2 a 2 b 2 4 × 4 2 3 a 3 4 =12 2 5 a 5 b 2 4 =12 × 2a 2a b 2 4 =24a 2a b 2 4
  3. 9 x 2 y 3 × 81 x 5 6 9 x 2 y 3 = (9 x 2 y ) 2 6 = 81 x 4 y 2 6 9 x 2 y 3 × 81 x 5 6 = 81 x 4 y 2 6 × 81 x 5 6 = 8 1 2 x 9 y 2 6 = ( 3 4 ) 2 x 9 y 2 6 = 3 8 x 9 y 2 6 =3x 3 2 x 3 y 2 6
  4. a 2 b 2 3 × 2 3 a 3 b 4 a 2 b 2 3 = ( a 2 b 2 ) 4 12 = a 8 b 8 12 2 3 a 3 b 4 =2 (3 a 3 b ) 3 12 =2 27 a 9 b 3 12 a 2 b 2 3 × 2 3 a 3 b 4 = a 8 b 8 12 × 2 27 a 9 b 3 12 =2 27 a 17 b 11 12 =2a 27 a 5 b 11 12
  5. 25 x 2 y 3 4 × 125 x 2 6 25 x 2 y 3 4 = ( 5 2 x 2 y 3 ) 3 12 = 5 6 x 6 y 9 12 125 x 2 6 = ( 5 3 x 2 ) 2 12 = 5 6 x 4 12 25 x 2 y 3 4 × 125 x 2 6 = 5 6 x 6 y 9 12 × 5 6 x 4 12 = 5 12 x 10 y 9 12 =5 x 10 y 9 12
  6. 2 3 4 m 2 3 × 3 4 16 m 4 n 5 2 3 4 m 2 3 = 2 3 ( 2 2 m 2 ) 5 15 = 2 3 2 10 m 10 15 3 4 16 m 4 n 5 = 3 4 ( 2 4 m 4 n ) 3 15 = 3 4 2 12 m 12 n 3 15 2 3 4 m 2 3 × 3 4 16 m 4 n 5 = 2 3 2 10 m 10 15 × 3 4 2 12 m 12 n 3 15 = 2 3 × 3 2 22 m 22 n 3 15 = 1 2 × 2 m 2 7 m 7 n 3 15 =m 2 7 m 7 n 3 15
  7. 1 2x × x 2 3 1 2x = 2x (2x ) 2 = 1 2x 2x = 1 2x (2x ) 3 6 = 1 2x 2 3 x 3 6 x 2 3 = ( x 2 ) 2 6 = x 4 6 1 2x × x 2 3 = 1 2x 2 3 x 3 6 × x 4 6 = 1 2x 2 3 x 7 6 = 1 2 x x 8x 6 = 1 2 8x 6
  8. 2x × 4x 5 × 1 16 x 2 10 2x = (2x ) 5 10 = 2 5 x 5 10 4x 5 = ( 2 2 x ) 2 10 = 2 4 x 2 10 2x × 4x 5 × 1 16 x 2 10 = 2 5 x 5 10 × 2 4 x 2 10 × 1 2 4 x 2 10 = 2 5 x 5 × 2 4 x 2 2 4 x 2 10 = 2 5 x 5 10 = (2x ) 5 = 2x
  9. 2 3 2b a × 3 8 a 2 4 b 2 3 2 3 2b a = 2 3 2b a × a a = 2 3a 2ab = 2 3a (2ab ) 3 6 = 2 3a 2 3 a 3 b 3 6 3 8 a 2 4 b 2 3 = 3 8 a 2 2 2 b 2 × 2b 2b 3 = 3 16b 2 a 2 b 3 = 3 16b (2 a 2 b ) 2 6 = 3 2 4 b 2 2 a 4 b 2 6 2 3 2b a × 3 8 a 2 4 b 2 3 = 2 3 a 2 3 a 3 b 3 6 × 3 2 b 2 2 a 4 b 2 6 = 1 2 3 ab 2 5 a 7 b 5 6 = 1 2 3 a b a 2 5 a b 5 6 = 1 8b 32a b 5 6
  10. 1 2 1 3 × 3 2 1 9 3 × 2436 1 2 1 3 = 1 2 ( 1 3 ) 3 6 = 1 2 1 3 3 6 3 2 1 9 3 = 3 2 ( 1 3 2 ) 2 6 = 3 2 1 3 4 6 1 2 1 3 × 3 2 1 9 3 × 2436 = 1 2 1 3 3 6 × 3 2 1 3 4 6 × 3 5 6 = 3 4 3 5 3 × 3 4 6 = 3 4 1 3 2 = 3 4 1 3 3