[tex]9)a) \frac{{[2.(6) - 2]}^{3} }{0.4} = \frac{10}{x} [/tex]
[tex] \frac{ {( \frac{26 - 2}{9} - 2)}^{3} }{ \frac{4}{10} } = \frac{10}{x} [/tex]
[tex] \frac{ {( \frac{24}{9} - 2)}^{3} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{ {( \frac{8}{3} - 2) }^{3} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{{( \frac{16}{6} - \frac{12}{6} )}^{3} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{ {( \frac{4}{6} )}^{3} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{ \frac{64}{216} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{ \frac{32}{108} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{ \frac{16}{54} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{ \frac{8}{27} }{ \frac{2}{5} } = \frac{10}{x} [/tex]
[tex] \frac{8x}{27} = \frac{20}{5}[/tex]
[tex] \frac{8x}{27} = 4[/tex]
[tex]x = \frac{4 \times 27}{8} [/tex]
[tex]x = \frac{27}{2} [/tex]
[tex]x = 13.5[/tex]
[tex]b) \frac{x}{{[2 - 1.(3)]}^{2} } = \frac{1.2}{0.8} [/tex]
[tex] \frac{x}{ {(2 - \frac{13 - 1}{9}) }^{2} } = \frac{ \frac{12}{10} }{ \frac{8}{10} } [/tex]
[tex] \frac{x}{ {(2 - \frac{11}{9} )}^{2} } = \frac{12}{8} [/tex]
[tex] \frac{x}{ {( \frac{18}{9} - \frac{11}{9}) }^{2} } = \frac{3}{2} [/tex]
[tex] \frac{x}{ {( \frac{7}{9}) }^{2} } = \frac{3}{2} [/tex]
[tex] \frac{x}{ \frac{49}{81} } = \frac{3}{2} [/tex]
[tex]x = \frac{3 \times \frac{49}{81} }{2} [/tex]
[tex]x = \frac{ \frac{49}{27} }{2} [/tex]
[tex]x = \frac{49}{54} [/tex]
[tex]10)a) \frac{ {3}^{100} - {3}^{99} - {3}^{98} }{x} = \frac{ {27}^{32} }{0.(3)} [/tex]
[tex] \frac{ {3}^{98} ( {3}^{2} - 3 - 1) }{x} = \frac{ {{(3}^{3} )}^{32} }{ \frac{3}{9} } [/tex]
[tex] \frac{ {3}^{98}(9 - 3 - 1) }{x} = \frac{ {3}^{96} }{ \frac{1}{3} } [/tex]
[tex] \frac{ {3}^{98} \times 5}{x} = \frac{ {3}^{96} }{ \frac{1}{3} } [/tex]
[tex]x = \frac{ \frac{ {3}^{98} \times 5 }{3} }{ {3}^{96} } [/tex]
[tex]x = \frac{ {3}^{97} \times \frac{5}{3} }{ {3}^{96} } [/tex]
[tex]x = \frac{ {3}^{96} \times 5}{ {3}^{96} } [/tex]
[tex]x = 5[/tex]
[tex]b) \frac{x}{ {2}^{51} - {2}^{50} - {2}^{49} } = \frac{0.(2)}{ ({{2}^{16})}^{3} } [/tex]
[tex] \frac{x}{ {2}^{49} ( {2}^{2} - 2 - 1)} = \frac{ \frac{2}{9} }{ {2}^{48} } [/tex]
[tex] \frac{x}{ {2}^{49} (4 - 2 - 1)} = \frac{ \frac{2}{9} }{ {2}^{48} } [/tex]
[tex] \frac{x}{ {2}^{49} \times 1 } = \frac{ \frac{2}{9} }{ {2}^{48} } [/tex]
[tex] \frac{x}{ {2}^{49} } = \frac{ \frac{2}{9} }{ {2}^{48} } [/tex]
[tex]x = \frac{ \frac{2 \times {2}^{49} }{9} }{ {2}^{48} } [/tex]
[tex]x = \frac{ \frac{ {2}^{50} }{9} }{ {2}^{48} } [/tex]
[tex]x = \frac{ {2}^{50} }{ {2}^{48} \times 9} [/tex]
[tex]x = {2}^{2} \times \frac{ {2}^{50} }{9} [/tex]
[tex]x = \frac{ {2}^{52} }{9} [/tex]
