Предмет: Алгебра, автор: BlessedFamq

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Ответы

Автор ответа: Miroslava227
2

Ответ:

1.

 \frac{ {(9 {x}^{2}) }^{2} \times  {x}^{ - 8}  }{ {x}^{ - 15}  \times 5 {x}^{9} }  = \frac{81 {x}^{4}  \times  {x}^{ - 8} }{5 {x}^{9 - 15} }   =  \\  =  \frac{81 {x}^{4 - 8} }{5 {x}^{ - 8} }  =  \frac{81 {x}^{ - 4 + 8} }{5}  =  \frac{81 {x}^{4} }{5}

2.

 \frac{ {(3x)}^{3} \times  {x}^{ - 9}  }{ {x}^{ - 10}  \times 2 {x}^{4} }  =   \frac{27 {x}^{3} \times  {x}^{ - 9 + 10 - 4}  }{2}  = \\  =  \frac{27 {x}^{3 - 3} }{2}  =  \frac{27}{2}  = 13.5

3.

 \frac{ {18}^{n} }{ {3}^{2n - 1}  \times  {2}^{n - 2} }  = \frac{ {9}^{n}  \times  {2}^{n} }{ {3}^{2 n- 1}  \times  {2}^{ n- 2} }    = \\  =   \frac{ {3}^{2n}  \times  {2}^{n - n + 2} }{ {3}^{2n - 1} }  =   {3}^{2n - 2n + 1}  \times  {2}^{2}  =  \\  = 3 \times 4 = 12

4.

 \frac{ {36}^{n} }{ {3}^{2n - 1}  \times  {4}^{n - 2} }  =  \frac{ {4}^{n}  \times  {9}^{n} }{ {3}^{2n - 1}  \times  {4}^{n - 2} }   = \\  =   \frac{ {4}^{2} \times  {3}^{2n}  }{ {3}^{2n - 1} }  = 16 \times 3 = 48

5.

 \frac{ {5}^{n + 1} -  {5}^{n - 1}  }{2 \times  {5}^{n} }  =  \frac{ {5}^{n - 1}( {5}^{2} - 1)  }{2 \times  {5}^{n} } =   \\  =  \frac{25 - 1}{5 \times 2}  =  \frac{24}{10}  = 2.4

6.

 \frac{10 \times  {2}^{n} }{ {2}^{n + 1}  +  {2}^{n - 1}  }  =  \frac{10 \times  {2}^{n} }{ {2}^{n - 1} ( {2}^{2} + 1) }   = \\  =  \frac{10 \times 2}{5}  = 4

7.

 \frac{ {2}^{n + 2} \times  {21}^{n + 3}  }{ {6}^{n + 1} \times  {7}^{n + 2}  }  = \frac{ {2}^{n + 2}  \times  {3}^{ n+ 3} \times  {7}^{n + 3}  }{ {2}^{n + 1} \times  {3}^{ n+ 1} \times  {7}^{ n+ 2}   } =    \\  =  \frac{2 \times  {3}^{2} \times 7 }{1}  = 14 \times 9 = 126

8.

 \frac{ {3}^{n + 3} \times  {16}^{n + 2}  }{ {12}^{n + 2} \times  {4}^{n + 1}  }  =  \frac{ {3}^{ n+ 2} \times  {4}^{ n+ 2} \times  {4}^{ n+ 2}   }{ {3}^{n + 2}  \times  {4}^{n + 2}  \times  {4}^{n + 1} } =   \\  =  \frac{4}{1}  = 4

9.

 \frac{8 \times  {100}^{n} }{ {2}^{2n + 1}  \times  {5}^{2n - 2} }  =  \frac{8 \times  {4}^{n}  \times  {25}^{n} }{ {2}^{2n + 1}  \times  {5}^{2n - 2} }  =  \\  =  \frac{ {2}^{3 + 2n }  \times  {5}^{2n} }{ {2}^{2n + 1}  \times  {5}^{2n - 2} }  =   {2}^{ 3 + 2n - 2n - 1}  \times  {5}^{2n - 2n + 2}  =  \\  =  {2}^{2}  \times  {5}^{2}  = 4  \times 25 = 100

10.

 \frac{4 \times  {36}^{n} }{ {3}^{2n - 3}  \times  {2}^{2n + 2} }  =    \frac{4 \times  {4}^{n}  \times  {9}^{n} }{ {3}^{2n - 3}  \times  {2}^{2 n+ 2} }  =  \\  =  \frac{ {2}^{2 + 2n}  \times  {3}^{2n} }{ {3}^{2 n- 3} \times  {2}^{2 n+ 2}  }  =  {2}^{2 + 2n - 2n - 2}  \times  {3}^{3}   = 27

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