Ejercicio 222

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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