[tex]a) \: \: \sqrt[4]{ {5}^{ \frac{1}{2} } } = {({5}^{ \frac{1}{2} } )}^{ \frac{1}{4} } = {5}^{ \frac{1}{8} } [/tex]
[tex]b) \: \: ({ \sqrt{5}) }^{3} = {({5}^{ \frac{1}{2} }) }^{3} = {5}^{ \frac{3}{2} } = {5}^{ 1\frac{1}{2} } [/tex]
[tex]c) \: \: \sqrt[3]{3} \div \sqrt[4]{3} = {3}^{ \frac{1}{3} } \div {3}^{ \frac{1}{4} } = {3}^{ \frac{4}{12} } \div {3}^{ \frac{3}{12} } = {3}^{ \frac{1}{12} } [/tex]
[tex]d) \: \: \sqrt[3]{3} \times \sqrt{3} = {3}^{ \frac{1}{3} } \times {3}^{ \frac{1}{2} } = {3}^{ \frac{2}{6} } \times {3}^{ \frac{3}{6} } = {3}^{ \frac{5}{6} } [/tex]
[tex]e) \: \: 2 \div {8}^{ \frac{2}{3} } = 2 \div {({2}^{3} )}^{ \frac{2}{3} } = 2 \div {2}^{2} = {2}^{ - 1} [/tex]
[tex]f) \: \: {2}^{ \frac{1}{2} } \times {4}^{ \frac{3}{2} } \div {8}^{ \frac{2}{3} } = {2}^{ \frac{1}{2} } \times{( {2}^{2} )}^{ \frac{3}{2} } \div {({2}^{3} )}^{ \frac{2}{3} } = {2}^{ \frac{1}{2} } \times {2}^{3} \div {2}^{2} = {2}^{ 1\frac{1}{2} } [/tex]
[tex]g) \: \: {3}^{ \frac{1}{8} } \times {12}^{ \frac{3}{4} } \div \sqrt{8} = {3}^{ \frac{1}{8} } \times {(3 \times 2 \times 2)}^{ \frac{3}{4} } \div {(2 \times 2 \times 2)}^{ \frac{1}{2} } = {3}^{ \frac{1}{8} } \times {3}^{ \frac{6}{8} } \times {2}^{ \frac{6}{4} } \div {2}^{ \frac{3}{2} } = {3}^{ \frac{7}{8} } \times {2}^{ \frac{3}{2} } \div {2}^{ \frac{3}{2} } = {3}^{ \frac{7}{8} } [/tex]
[tex]h) \: \: {3}^{ \frac{1}{2} } \times {9}^{ \frac{1}{3} } \times \sqrt{3} = {3}^{ \frac{1}{2} } \times {( {3}^{2}) }^{ \frac{1}{3} } \times {3}^{ \frac{1}{2} } = 3 \times {3}^{ \frac{2}{3} } = {3}^{1 \frac{2}{3} } [/tex]
Mam nadzieję, że pomogłam! ❤️
