Question

в 4.4 задание б
в 4.6 всё. дам 45балов​

Answer 1

4.4.

б)

${a}^{1 \frac{2}{3} } = {a}^{ \frac{5}{3} } = \sqrt[3]{ {a}^{5} } \\ {c}^{1.4} = {c}^{1 \frac{2}{5} } = c {}^{ \frac{7}{5} } = \sqrt[5]{ {c}^{7} } \\ {x}^{ \frac{1}{n} } = \sqrt[n]{x} \\ {x}^{ \frac{n}{2} } = \sqrt{ {x}^{n} } \\ y {}^{ \frac{m}{n} } = \sqrt[n]{ {y}^{m} }$

4.6

а)

$25 {}^{ \frac{1}{2} } = \sqrt{25} = \sqrt{ {5}^{2} } = 5 \\ {49}^{ \frac{1}{2} } = \sqrt{49} = \sqrt{ {7}^{2} } = 7 \\ 27 {}^{ \frac{1}{3} } = \sqrt[3]{27} = \sqrt[3]{ {3}^{3} } = 3 \\ {16}^{0.25} = {16}^{ \frac{1}{4} } = \sqrt[4]{16} = \sqrt[4]{ {2}^{4} } = 2 \\ {100}^{0.5} = {100}^{ \frac{1}{2} } = \sqrt{100} = \sqrt{10 {}^{2} } = 10$

б)

${16}^{ \frac{3}{4} } = \sqrt[4]{16 {}^{3} } = \sqrt[4]{(2 {}^{3} ) {}^{4} } = {2}^{3} = 8 \\ {27}^{ \frac{2}{3} } = \sqrt[3]{27 {}^{2} } = \sqrt[3]{( {3}^{2}) {}^{3} } = {3}^{2} = 9 \\ {25}^{2.5} = {25}^{ \frac{5}{2} } = \sqrt{ {25}^{5} } = \sqrt{( {5}^{5} ) {}^{2} } = {5}^{5} =3 125 \\ {8}^{ \frac{5}{3} } = \sqrt[3]{ {8}^{5} } = \sqrt[3]{( {2}^{5} ) {}^{3} } = {2}^{5} = 32 \\ {27}^{ \frac{4}{3} } = \sqrt[3]{27 {}^{4} } = \sqrt[3]{( {3}^{4} ) {}^{3} } = {3}^{4} = 81$