[tex]\displaystyle\\
\left[\left(5 \frac{8}{15} -3 \frac{21}{45}\right)\times 4,5-2 \frac{1}{6}:0,52- \frac{69}{15}\right]^2 =\\\\
=\left[\left(\frac{5\times15+8}{15} -\frac{3\times45+21}{45}\right)\times \frac{45}{10} -\frac{2\times 6+1}{6}:\frac{52}{100} - \frac{69}{15}\right]^2 =\\\\
=\left[\left(\frac{83}{15} -\frac{156}{45}\right)\times \frac{45}{10} -\frac{13}{6}:\frac{52}{100} - \frac{69}{15}\right]^2 =\\\\
[/tex]
[tex]\displaystyle\\
=\left[\left(\frac{83\times3}{15\times3} -\frac{156}{45}\right)\times \frac{45}{10} -\frac{13}{6}\times\frac{100}{52} - \frac{69}{15}\right]^2 =\\\\
=\left[\left(\frac{249}{45} -\frac{156}{45}\right)\times \frac{45}{10} -\frac{13\times 100}{6\times 52} - \frac{69}{15}\right]^2 =\\\\
=\left[\frac{249-156}{45} \times \frac{45}{10} -\frac{13\times25\times 4}{6\times 13 \times 4} - \frac{69}{15}\right]^2 =\\\\
[/tex]
[tex]\displaystyle\\
=\left[\frac{93}{45} \times \frac{45}{10} -\frac{25}{6} - \frac{23}{5}\right]^2 =\\\\
=\left[\frac{93}{10} -\frac{25}{6} - \frac{23}{5}\right]^2 =\\\\
=\left[\frac{93\times3}{30} -\frac{25\times5}{30} - \frac{23\times6}{30}\right]^2 =\\\\
=\left[\frac{279-125-138}{30}}\right]^2 =\\\\
=\left[\frac{16}{30}}\right]^2 =\left[\frac{8}{15}}\right]^2 =\frac{8^2}{15^2}= \boxed{\bf \frac{64}{225}}[/tex]
