[tex]c)0. {4}^{7} \times 2. {5}^{ - 4} \div ( \frac{2}{5} {)}^{5} = (\frac{2}{5} {)}^{7} \times ( \frac{5}{2} {)}^{ - 4} \div ( \frac{2}{5} {)}^{5} = ( \frac{2}{5} {)}^{7} \times ( \frac{2}{5} {)}^{4} \div ( \frac{2}{5} {)}^{5} = ( \frac{2}{5} {)}^{7 + 4 - 5} = ( \frac{2}{5} {)}^{6} [/tex]
[tex]d)0.6 {4}^{5} \div 1.2 {5}^{ - 4} \times 0. {8}^{ - 2} = ( \frac{16}{25} {)}^{5} \div ( \frac{5}{4} {)}^{ - 4} \times (\frac{4}{5} {)}^{ - 2} = ( \frac{4}{5} {)}^{10} \div ( \frac{4}{5} {)}^{4} \times ( \frac{4}{5} {)}^{ - 2} = ( \frac{4}{5} {)}^{10 - 4 - 2} = ( \frac{4}{5} {)}^{4} [/tex]
[tex]e) \sqrt{2} \times \sqrt[3]{2} \div \sqrt{8} = {2}^{ \frac{1}{2} } \times {2}^{ \frac{1}{3} } \div {8}^{ \frac{1}{2} } = {2}^{ \frac{1}{2} } \times {2}^{ \frac{1}{3} } \div {2}^{ \frac{3}{2} } = {2}^{ \frac{1}{2} + \frac{1}{3} - \frac{3}{2} } = {2}^{ \frac{3}{6} + \frac{2}{6} - \frac{9}{6} } = {2}^{ - 4} [/tex]
[tex]f) {9}^{ \frac{2}{3} } \times \sqrt[4]{ {27}^{2} } = \sqrt[3]{ {9}^{2} } \times \sqrt[4]{ {27}^{2} } = \sqrt[12]{ {9}^{8} } \times \sqrt[12]{ {27}^{6} } = \sqrt[12]{ {3}^{16} \times {3}^{18} } = \sqrt[12]{ {3}^{34} } = \sqrt[6]{ {3}^{17} } = {3}^{ \frac{17}{6} } [/tex]
