Question

Calcular as potências
utilizando alguma propriedade:


a)   
[(-3)²]-¹     
b) [-(½)³]-²  
c) 10-³÷10-6     
        10-²  
d) 105.10-²÷10-1     
       10-³
÷10

Answer 1

Calcular as potências
utilizando alguma propriedade

a)
[(-3)²]-¹
                                                   1           1
[(-3)²]-¹  =[9]-¹ = 9-¹ =  1/9¹  =     ----   =  -----  
                                                   9¹          9



b) [-(½)³]-²
                                                   1-²                    8²          64
  [-(1/2)³]-² = [- 1/8] -²     =    -   -------   inverte    ----  =     ---- = 64
                                                    8-²                   1²           1


c) 10-³÷10-6
        10-² 

                               1                       1                        1   ( 1 )                 1
                             ----   : 4             -----  : 4               -----------              -----
10-³ : 10 - 6            10³                  1000                    4(1000)             4000  
---------------- =  ---------------- = ----------------------- = ---------------=  --------------- =
      10-²                   1                       1                            1                      1
                               ----                    ----                         -----                 -----
                               10²                   100                         100                 100

conserva e 1ª e multiplica invertendo a 2º


      1              100        100         1
---------- x      ------- =   ------- =   -----    =  0,025
 4000               1         4000        40




d) 105.10-²÷10-1      colega  onde fica o : 10???? 
              10-³
÷10

Answer 2

a )

$[(-3)^2]^{-1}~\to~[(9)]^{-1}~\to~ \frac{1}{9}~\to~3^{-2}$

b )

$\boxed{[-( \frac{1}{2} )^3]^{-2}~\to~[- \frac{1}{8} ]^{-2}~\to~ \frac{1}{(- \frac{1}{8})^{2}}\to\frac{1}{ \frac{1}{64}}=64}$

c )

$\boxed{ \frac{10^{-3}\div10^{-6}}{10^{-2}} \to~ \frac{10^{-3-(-6)}}{10^{-2}}~\to~ \frac{10^{3}}{10^{-2}}~\to~10^5}$

d ) Não compreensível