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Najlepsze rozwiązanie

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  ewka13 19.9.2011 (11:26)

  a)
  (3^{2})^{3} : 3^{5} = 3^{6} : 3^{5} = 3
  
  b)
  (\frac {5^{4}} {5^{2}})^{2} = (5^{2})^{2} =5^{4}=625
  
  c)
  (\frac {2} {5})^{7}\cdot 2,5^{6} = (\frac {1} {2,5})^{7} \cdot 2,5^{6} =
  
  =\frac {1} {2,5^{7}} \cdot 2,5^{6} =\frac {1} {2,5} = \frac {2} {5}
  
  d)
  \frac {4^{5}} {2^{7}}\cdot 5^{3} =\frac {(2^{2})^{5}} {2^{7}}\cdot 5^{3} =
  
  =\frac {2^{10}} {2^{7}}\cdot 5^{3} =2^{3} \cdot 5^{3}= (2\cdot 5)^{3} =10^{3}=1000
  
  e)
  \frac {9^{3}\cdot 4^{4}} {6^{10}} =\frac {(3^{2})^{3}\cdot (2^{2})^{4}} {6^{10}}=
  
  =\frac {3^{6}\cdot 2^{8}} {3^{10}\cdot 2^{10}}=\frac {1} {2^{2}\cdot 3^{4}}=
  
  =\frac {1} {4\cdot 81}=\frac {1} {324}
  
  f)
  \frac {0,25^{3} : 0,5^{3}} {5^{3}} =\frac {(0,25 : 0,5)^{3}} {5^{3}} = \frac {0,5^{3}} {5^{3}}=
  
  =(0,5 : 5)^{3} = 0,1^{3} = 0,001.

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