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$1)\frac{(4^4)^{24}}{4^{97}} =\frac{(4^{4*24}}{4^{97}}=\frac{4^{96}}{4^{97}} =\frac{1}{4} \\ \\ 2)(512^9)^4:(64^9)^6=512^{36}:64^{54}=(8^3)^{36}:(8^2)^{54}=8^{108}:8^{108}=1\\ \\ 3)\frac{2}{5} -(\frac{52}{100} *\frac{5}{26})=\frac{2}{5} -(\frac{13}{25} *\frac{5}{26}) =\frac{2}{5} -(\frac{1}{5} *\frac{1}{2} )=\frac{2}{5} -\frac{1}{10} =\frac{4-1}{10} =\frac{3}{10} =0,3\\ \\ 4)\frac{37}{100} +(\frac{7}{20} *\frac{9}{5} )=\frac{37}{100} +\frac{63}{100}=\frac{37+63}{100} =\frac{100}{100} =1$