Question

Помогите пожалуйста!

Answer 1

Ответ:

21. 2

22. 1

23. 2

24. 4

25. 2

26. 4

27. 4

Пошаговое объяснение:

21.

${( \frac{ {x}^{ - \frac{1}{2} } \times {x}^{ \frac{1}{3} } }{ \sqrt{x} \times {x}^{ - \frac{1}{3} } } )}^{ \frac{3}{4} } = {( {x}^{ - \frac{1}{2} - \frac{1}{2} } \times {x}^{ \frac{1}{3} + \frac{1}{3} } )}^{ \frac{3}{4} } = \\ = {( {x}^{ - 1 + \frac{2}{3} } )}^{ \frac{3}{4} } = {( {x}^{ - \frac{1}{3} } )}^{ \frac{3}{4} } = \\ = {x}^{ - \frac{1}{4} } = \\ \\ = {(0.0625)}^{ - \frac{1}{4} } = \sqrt[4]{ \frac{10000}{625} } = \\ = \frac{10}{5} = 2$

22.

$\frac{ {3}^{ \frac{1}{2} } \times {2}^{ \frac{1}{2} } }{ \sqrt[4]{36} } = \frac{ {6}^{ \frac{1}{2} } }{ \sqrt[4]{ {6}^{2} } } = \frac{ {6}^{ \frac{1}{2} } }{ {6}^{ \frac{1}{2} } } = 1$

23.

$\frac{ {a}^{ \frac{2}{3} } - 16 }{ {a}^{ \frac{1}{3} } - 4 } - { a}^{ \frac{1}{3} } = \frac{ {a}^{ \frac{2}{3} } - 16 - {a}^{ \frac{1}{3} }( {a}^{ \frac{1}{3} } - 4) }{ {a}^{ \frac{1}{3} } - 4} = \\ = \frac{ {a}^{ \frac{2}{3} } - 16 - {a}^{ \frac{2}{3} } + 4 {a}^{ \frac{1}{3} } }{ {a}^{ \frac{1}{3} } - 4 } = \frac{4( {a}^{ \frac{1}{3} } - 4)}{ {a}^{ \frac{1}{3} } - 4 } = 4$

24.

${a}^{ \frac{1}{4} } \div {a}^{ - 0.75} = {a}^{ \frac{1}{4} - ( - \frac{3}{4} )} = {a}^{1} = a$

25.

${a}^{ - 1 \frac{1}{2} } \div {a}^{ - \frac{6}{7} } = {a}^{ - \frac{3}{2} + \frac{6}{7} } = {a}^{ \frac{ - 21 + 12}{14} } = \\ = {a}^{ - \frac{9}{14} }$

26.

${9}^{3p} \times {3}^{ - \frac{1}{p} } = {3}^{6p} \times {3}^{ - \frac{1}{p} } = {3}^{6p - \frac{1}{p} } = \\ \\ = {3}^{3 - 2} = {3}^{1} = 3$

27.

${3}^{ - 6p} \times \frac{1}{ {3}^{ - 4p} } = {3}^{ - 6p} \times {3}^{4p} = {3}^{ - 2p} = \\ \\ = {3}^{4} = 81$