Question

Дайте пожалуйста ответы, даю 38 баллов

Answer 1

Объяснение:

1

$1)24 \times {2}^{ - 5} + {5}^{2} \times {125}^{ - 1} = 3 \times {2}^{3} \times {2}^{ - 5} + {5}^{2} \times {( {5}^{3} )}^{ - 1} = \frac{3 \times {2}^{3} }{ {2}^{ 5} } + \frac{ { 5 }^{2} }{ {5}^{3} } = \frac{3}{ {2}^{2} } + \frac{1}{5} = \frac{3}{4} + \frac{1}{5} = \frac{15 + 4}{20} = \frac{19}{20} = \frac{95}{100} = 0.95$

$2)7 \times {(3.5)}^{ - 1} - {(0.01)}^{ - 2} =7 \times \frac{1}{3.5} - \frac{ {1}^{ - 2} }{100 {}^{ - 2} } =7 \times \frac{10}{35} - \frac{10000}{1} = \frac{10}{5} - \frac{10000}{1} = 2 - 10000 = - 9998$

2.

$0.2 {b}^{ - 5} = \frac{2}{10} \times {b}^{ - 5} = \frac{2}{10} \times \frac{1}{b {}^{5} } = \frac{1}{5 {b}^{5} }$

$( {x}^{ - 3} (1 + y) {)}^{ - 2} = ( \frac{1 + y}{ {x}^{3} } {)}^{ - 2} = ( \frac{ {x}^{3} }{1 + y} {)}^{2} = \frac{ {x}^{6} }{1 + 2y + {y}^{2} }$

${a}^{ - 4} - 2 {a}^{ - 5} = \frac{1}{ {a}^{4} } - \frac{2}{ {a}^{5} } = \frac{a - 2}{ {a}^{5} }$

3.

$1250 = 1.25 \times {10}^{3}$

$0.000011 = \frac{11}{1000000} = \frac{11}{ {10}^{6} } = 11 \times {10}^{ - 6} = 1.1 \times {10}^{ - 5}$

4.

$(4.5 {)}^{ - 3} \: i \: ( \frac{4}{81} ) {}^{3} \\( \frac{9}{2} {)}^{ - 3} \: i \: ( \frac{4}{81} {)}^{3} \\ ( \frac{ {3}^{2} }{2} {)}^{ - 3} \: i \:( \frac{ {2}^{2} }{ {3}^{4} } {)}^{3} \\ ( \frac{2}{ {3}^{2} } {)}^{3} \: i \:( \frac{ {2}^{2} }{ {3}^{4} } {)}^{3} \\ \frac{2}{ {3}^{2} } \: i \: \frac{ {2}^{2} }{ {3}^{4} } \\ \frac{2 \times {3}^{2} }{ {3}^{4} } \: i \: \frac{ {2}^{2} }{ {3}^{4} } \\ \frac{ 18}{ {3}^{4} } > \frac{4}{ {3}^{4} } \\ \\ (4.5 {)}^{ - 3} > ( \frac{4}{81} {)}^{3}$