Question

Calcule o valor de cada potencia:

(0,2)³ = ? (1,5)² =? (2,5) 4 = ? (0,222...)² =? (1,5555...)²=? (

(1,333...)³=?

Answer 1

Calcule o valor de cada potencia:

(0,2)³ = ?

(0,2)³ = (0,2)(0,2)(0,2) = 0,008
⁴⁴
 (1,5)² =?
(1,5)² = (1,5)(1,5) = 2,25

(2,5) 4
(2,5)⁴ = (2,5)(2,5)(2,5)(2,5) =39,0625

  (0,222...)²     atenção  dizima periodica em FRAÇÃO irredutiveL


       x =     0,222...( 10) muiltiplica
    10x =    2,222...
 
 10x = 2,222...
     x = 0,222... SUBTRAI
---------------------------------
   9x =  2,000...

9x = 2
x = 2/9

assim

(0,222...)² = (2/9)² = (2²/9²) = 2x2/9x9 = 4/81

 
  (1,5555...)²=? 


                  x      =     1,555...(10) multiplica
              10x      =   15,555...   

10x = 15,555...
    x  =  1,555...subtrai
----------------------------------
  9x = 14,000....

9x = 14
x = 14/9

assim

(1,555...)² = (14/9)² =  14²/9²  = 14x14/9x9  = 196/81
 
(1,333...)³=?
 
                     x   =    1,333... (10) multiplica
                 10x   =  13,333...

10x = 13,333...
   x  =   1,333... subtrai
---------------------------------
 9x  = 12,000...

9x = 12
x = 12/9

assim
(1,333)³ = (12/9)³ = 12³/9³  = 12x12x12/9x9x9  = 1728/729

1728/729  = (divide AMBOS 27)
64/27

ASSIM

(1,333...)³ = 1728/729

ou

(1,333...)³ = 64/27