Question

Помогите пожалуйста, буду очень благодарен!

Answer 1

Ответ:

1.

$\frac{ {(5 {a}^{2} )}^{3} \times {(6b)}^{2} }{ {(30 {a}^{3} {b} )}^{2} } = \frac{125 {a}^{6} \times 36 {b}^{2} }{900 {a}^{6} {b}^{2} } = \frac{125 \times 36}{900} = \\ = 5$

2.

$\frac{9 {x}^{2} - 4 }{3x + 2} - 3x = \frac{9 {x}^{2} - 4 - 3x(3x + 2) }{3x + 2} = \\ = \frac{9 {x}^{2} - 4 - 9 {x}^{2} - 6x }{3x + 2} = \frac{ - 6x - 4}{3x + 2} = \\ = \frac{ - 2(3x + 2)}{3x + 2} = - 2$

3.

$( \sqrt{3 \frac{6}{7} } - \sqrt{1 \frac{5}{7} } ) \div \sqrt{ \frac{3}{28} } = \\ = ( \sqrt{ \frac{27}{7} } - \sqrt{ \frac{12}{7} } ) \times \sqrt{ \frac{28}{3} } = \\ = \sqrt{ \frac{27}{7} } \times \sqrt{ \frac{28}{3} } - \sqrt{ \frac{12}{7} } \times \sqrt{ \frac{28}{3} } = \\ = \sqrt{ \frac{9 \times 4}{1} } - \sqrt{ \frac{4 \times 4}{1} } = \\ = 6 - 4 = 2$

4.

$8 \sqrt[3]{ {a}^{4} } \div 2 \sqrt[3]{ {a}^{7} } = 4( {a}^{ \frac{4}{3} } \div {a}^{ \frac{7}{3} } ) = 4 {a}^{ \frac{4}{3} - \frac{7}{3} } = \\ = 4 {a}^{ - 1} = \frac{4}{ {a}}$

5.

$\frac{15 \sqrt[5]{ \sqrt[28]{a} } - \sqrt[7]{ \sqrt[20]{a} } }{2 \sqrt[35]{ \sqrt[4]{a} } } = \frac{15 {a}^{ \frac{1}{28} \times \frac{1}{5} } - {a}^{ \frac{1}{20} \times \frac{1}{7} } }{2 {a}^{ \frac{1}{4} \times \frac{1}{35} } } = \\ = \frac{15 {a}^ { \frac{1}{140} } - {a}^{ \frac{1}{140} } }{2 { a}^{ \frac{1}{140} } } = \frac{ {a}^{ \frac{1}{140} }(15 - 1) }{2 {a}^{ \frac{1}{140} } } = \\ = \frac{14}{2} = 7$

6.

$\frac{ {2}^{1 + 2 log_{2}(5) } }{ {16}^{ log_{2}(5) } } = \frac{2 \times {2}^{ log_{2}( {5}^{2} ) } }{ {2}^{4 log_{2}(5) } } = \\ = \frac{2 \times {5}^{2} }{ {2}^{ log_{2}( {5}^{4} ) } } = \frac{2 \times 25}{25 \times 25} = \frac{2}{25}$

7.

${36}^{ log_{6}(5) } + {10}^{ log_{10}(2) } - {3}^{ log_{9}(36) } = \\ = {6}^{2 log_{6}(5) } + 2 - {3}^{ log_{ {3}^{2} }(36) } = \\ = {6}^{ log_{6}( {5}^{2} ) } + 2 - {3}^{ \frac{1}{2} log_{3}(36) } = \\ = 25 + 2 - {3}^{ log_{3}( {36}^{ \frac{1}{2} } ) } = \\ = 27 - 6 = 21$