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CAPITULO XXXI

R a d i c a l e s
Potenciación de radicales
Ejercicio 245
Desarollar:
  1. (4 2 ) 2 = 4 2 2 2 =16 × 2 =32
  2. (2 3 ) 2 = 2 2 3 2 =4 × 3 =12
  3. (5 7 ) 2 = 5 2 7 2 =25 × 7 =175
  4. (2 43 ) 2 = 2 2 4 2 3 =4 2 4 3 =4 × 2 23 =8 23
  5. (3 2 a 2 b 3 ) 4 = 3 4 (2 a 2 b ) 4 3 =81 2 4 a 8 b 4 3 =81 × 2 a 2 b 2 a 2 b 3 =162 a 2 b 2 a 2 b 3
  6. ( 8 x 3 4 ) 2 = ( 2 3 x 3 ) 2 4 = 2 6 x 6 4 =2x (2x ) 2 =2x 2x
  7. ( 81a b 3 5 ) 3 = ( 9 2 a b 3 ) 3 5 = 9 6 a 3 b 9 5 =9b 9 a 3 b 4 5
  8. (186 ) 3 = 1 8 3 = 18 = 3 2 × 2 =3 2
  9. (4a 2x ) 2 = (4a ) 2 (2x ) 2 = 2 4 a 2 × 2x = 2 5 a 2 x =32 a 2 x
  10. (2 x+1 ) 2 = 2 2 (x+1 ) 2 =4(x+1 ) =4x+4
  11. (3 xa ) 2 = 3 2 (xa ) 2 =9(xa ) =9x9a
  12. (4 9 a 3 b 4 6 ) 3 = 4 3 (9 a 3 b 4 ) 3 = 2 6 3 2 a 3 b 4 = 2 6 × 3a b 2 a =192a b 2 a
    Elevar al cuadrado:
  13. 2 3 = ( 2 3 ) 2 =22 2 × 3 +3 =52 6
  14. 4 2 + 3 = (4 2 + 3 ) 2 = (4 2 ) 2 +8 2 × 3 +3 = 2 4 2+8 6 +3 = 2 5 +8 6 +3 =32+8 6 +3 =35+8 6
  15. 5 7 = ( 5 7 ) 2 =52 5 × 7 +7 =122 35
  16. 5 7 6 = (5 7 6 ) 2 = (5 7 ) 2 2 × 5 7 × 6+36 =25 × 760 7 +36 =17560 7 +36 =21160 7
  17. x + x1 = ( x + x1 ) 2 = (x ) 2 +2 x × x1 + ( x1 ) 2 =x+2 x 2 x +x1 =2x+2 x 2 x 1
  18. x+1 4 x = ( x+1 4 x ) 2 = ( x+1 ) 2 2 x+1 × 4 x + (4 x ) 2 =x+18 x 2 +x +16x =17x8 x 2 +x +1
  19. a+1 a1 = ( a+1 a1 ) 2 = ( a+1 ) 2 2 a+1 × a1 + ( a1 ) 2 =a+ 1 2 a 2 1 +a 1 =2a2 a 2 1
  20. 2 2x1 + 2x+1 = (2 2x1 + 2x+1 ) 2 = (2 2x1 ) 2 +2 × 2 2x1 × 2x+1 + ( 2x+1 ) 2 =4(2x1 ) +4 4 x 2 1 +2x+1 =8x4+4 4 x 2 1 +2x+1 =10x+4 4 x 2 1 3