[latex]displaystyle\ left[left(5 frac{8}{15} -3 frac{21}{45} ight) imes 4,5-2 frac{1}{6}:0,52- frac{69}{15} ight]^2 =\\ =left[left(frac{5 imes15+8}{15} -frac{3 imes45+21}{45} ight) imes frac{45}{10} -frac{2 imes 6+1}{6}:frac{52}{100} - frac{69}{15} ight]^2 =\\ =left[left(frac{83}{15} -frac{156}{45} ight) imes frac{45}{10} -frac{13}{6}:frac{52}{100} - frac{69}{15} ight]^2 =\\ [/latex] [latex]displaystyle\ =left[left(frac{83 imes3}{15 imes3} -frac{156}{45} ight) imes frac{45}{10} -frac{13}{6} imesfrac{100}{52} - frac{69}{15} ight]^2 =\\ =left[left(frac{249}{45} -frac{156}{45} ight) imes frac{45}{10} -frac{13 imes 100}{6 imes 52} - frac{69}{15} ight]^2 =\\ =left[frac{249-156}{45} imes frac{45}{10} -frac{13 imes25 imes 4}{6 imes 13 imes 4} - frac{69}{15} ight]^2 =\\ [/latex] [latex]displaystyle\ =left[frac{93}{45} imes frac{45}{10} -frac{25}{6} - frac{23}{5} ight]^2 =\\ =left[frac{93}{10} -frac{25}{6} - frac{23}{5} ight]^2 =\\ =left[frac{93 imes3}{30} -frac{25 imes5}{30} - frac{23 imes6}{30} ight]^2 =\\ =left[frac{279-125-138}{30}} ight]^2 =\\ =left[frac{16}{30}} ight]^2 =left[frac{8}{15}} ight]^2 =frac{8^2}{15^2}= oxed{f frac{64}{225}}[/latex]