[tex] \frac{2}{7} \times \frac{14}{10} + \frac{4}{9} : \frac{10}{9} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2 \times 14}{7 \times 10} + \frac{4}{9} : \frac{10}{9} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{28}{70} + \frac{4}{9} : \frac{10}{9} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2}{5} + \frac{4}{9} : \frac{10}{9} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2}{5} + \frac{4}{9} \times \frac{9}{10} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2}{5} + \frac{4 \times 9}{10 \times 9} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2}{5} + \frac{36}{90} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2}{5} + \frac{2}{5} + \frac{ {5}^{2} }{ {5}^{3} } = \frac{2}{5} + \frac{2}{5} + {5}^{2 - 3} = \frac{2}{5} + \frac{2}{5} + {5}^{ - 1} = \frac{2}{5} + \frac{2}{5} + \frac{1}{5} = 1 [/tex]
