Treść zadania

Rozwiązania

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  0 0

  turtle 24.8.2012 (11:49)

  a)
  (2^{2})^{-3} = 4 ^ {-3} = (\frac{1}{4} )^{3} = \frac{1}{64}
  
  b)
  (2^{-3})^{-2} = ((\frac{1}{2} )^{3} )^{-2} = (\frac{1}{8} )^{-2} = 8^2 = 64
  lub prościej: (2^{-3})^{-2} = 2 ^ {-3*-2} = 2^{6} = 64
  
  c)
  ((-1/2)^{2})^{-3} = (\frac{1}{4} )^{-3} = 4 ^{3} = 64
  
  
  d)
  ((-2)^{-3})^{-2} = ((-\frac{1}{2} )^{3} ) ^ {-2} = (-(\frac{1}{8} ))^{-2} = -8 ^ {2} = 64
  lub prościej: (-2^{-3*-2}) = (-2 )^ {6} = 64
  
  e)
  ((-2)^{2})^{-3} = 4 ^ {-3} = (\frac{1}{4} )^{3} ) = \frac{1}{64}
  
  f)
  ((1/2)^{-2} = 2^{2} = 4
  
  g)
  ((-0,1)^{-2})^{-4} = ((-\frac{1}{10} )^{-2} ) ^ {-4} = (-\frac{1}{10} )^{-2*-4} = (-\frac{1}{10} )^{8} ) = \frac{1}{10^{8}}
  
  h)
  ((-0,1)^{-4})^{2} = (z_powyzszego_przykladu) = (-\frac{1}{10} )^{-8} ) =
  -10 ^ {8} = 10^{8} = 100 000 000
  
  i)
  ((-1)^{-3})^{-6} = (-1)^{-3*-6} = (-1) ^ {18} = 1
  
  j)
  ((-1)^{6})^{-3} = (-1)^{6*-3} = (-1) ^ {-18} = -1

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