[tex]{({5 \frac{2}{5} })}^{4} \times ({ \frac{5}{9} )}^{4} = \\ ({ \frac{27}{5}) }^{4} \times ( \frac{5}{9} ) {}^{4} = \\ \frac{ {27}^{4} \times {5}^{4} }{ {5}^{4} \times {9}^{4} } = \\ \frac{( {3}^{3} ) {}^{4} }{( {3}^{2} ) {}^{4} } = \frac{ {3}^{12} }{ {3}^{8} } = \\ {3}^{12 - 8} = {3}^{4} = 81[/tex]
