[tex]a) \: ( { \frac{1}{4} })^{5} \div \frac{1}{ {2}^{8} } = \frac{1}{1024} \times {2}^{8} = \\ \\ \frac{1}{ {2}^{10} } \times {2}^{8} = \frac{1}{ {2}^{2} } = \frac{1}{4} = 0.25[/tex]
[tex]b) \: \frac{( { - 6})^{4} \times ( { - 2})^{4} }{ {12}^{2} } = \frac{ {6}^{4} \times {2}^{4} }{ {2}^{2} \times {6}^{2} } = \\ \\ {6}^{2} \times {2}^{2} = {12}^{2} = 144[/tex]
[tex] \\ c) \: {2}^{9} \div ( - {6}^{7} \div {3}^{7} ) = {2}^{9} \div ( - {2}^{7} ) = \\ - {2}^{2} = - 4[/tex]
[tex] \\ d) \: \frac{ {32}^{3} }{ {8}^{2} } = \frac{ {2}^{15} }{ {2}^{6} } = {2}^{9} = 512[/tex]
[tex] \\ e) \: \frac{ {81}^{4} }{ {27}^{5} } = \frac{ {3}^{16} }{ {3}^{15} } = 3[/tex]
[tex] \\ f) \: \frac{ {25}^{2} \times {4}^{7} }{ {2}^{9} \times {5}^{4} } = \frac{ {5}^{4} \times {2}^{14} }{ {2}^{9} \times {5}^{4} } = \\ \\ \frac{ {2}^{14} }{ {2}^{9} } = {2}^{5} = 32 \\ [/tex]
[tex] \\ g) \: \frac{ {2}^{10} \times {3}^{10} }{ {6}^{8} } = \frac{ {2}^{10} \times {3}^{10} }{ {3}^{8} \times {2}^{8} } = \\ \\ {2}^{2} \times {3}^{2} = {6}^{2} = 36[/tex]
[tex] \\ h) \: \frac{ {5}^{8} \times {2}^{9} }{ {10}^{7} } = \frac{ {5}^{8} \times {2}^{9} }{ {2}^{7} \times {5}^{7} } = \\ \\ 5 \times {2}^{2} = 5 \times 4 = 20[/tex]
