Question

Помогите, пожалуйста

Answer 1

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.

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