1, Đặt \(A=\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

\(A=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)\(A=\frac{2^{28}\left(5.2^2.3^{18}-2.3^{20}\right)}{2^{28}\left(5.3^{19}-7.2.3^{18}\right)}\)

\(A=\frac{5.2^2.3^{18}-2.3^{20}}{5.3^{19}-7.2.3^{18}}\)\(A=\frac{3^{18}\left(5.2^2-2.3^2\right)}{3^{18}\left(5.3-7.2\right)}\)

\(A=\frac{5.2^2-2.3^2}{5.3-7.2}\)\(A=2\)

\(1\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)

\(\Rightarrow\frac{31}{30}:\left(\frac{145}{6}-\frac{121}{5}\right)-\frac{\frac{3}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{41}{5}-\frac{25}{3}\right)\)

\(\Rightarrow\frac{31}{30}:\left(\frac{725}{30}-\frac{726}{30}\right)-\frac{\frac{6}{4}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{123}{15}-\frac{125}{15}\right)\)

\(\Rightarrow\frac{31}{30}:\frac{-1}{30}-\frac{\frac{3}{4}}{4x-\frac{1}{2}}=\frac{-16}{15}:\frac{-2}{15}\)

\(\Rightarrow\frac{31}{30}.\frac{30}{-1}-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\frac{-16}{15}.\frac{15}{-2}\)

\(\Rightarrow\left(-31\right)-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=8\)

\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-31\right)-8\)

\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-39\right)\)

\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}:\left(-39\right)\)

\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}.\frac{-1}{39}\)

\(\Rightarrow4x-\frac{1}{2}=\frac{-1}{52}\)

\(\Rightarrow4x=\frac{-1}{52}+\frac{1}{2}\)

\(\Rightarrow4x=\frac{-1}{52}+\frac{26}{52}\)

\(\Rightarrow4x=\frac{25}{52}\)

\(\Rightarrow x=\frac{25}{52}:4\)

\(\Rightarrow x=\frac{25}{52}.\frac{1}{4}\)

\(\Rightarrow x=\frac{25}{208}\)

Vậy \(x=\frac{25}{208}\)

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