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\(D=\log_{5^{-1}}\left(5^2\right)-3\log_{3^2}\left(3^{-1}\right)+4.\log_{2^{\frac{3}{2}}}2^6=-2+\frac{3}{2}+16=\frac{31}{2}\)
\(B=25^{\frac{1}{2}+\frac{1}{9}\log_{\frac{1}{2}}27+\log_{125}81}=\left(5^2\right)^{\frac{1}{2}+\frac{1}{9}\log_{5^{-1}}3^3+\log_{5^3}3^4}\)
\(=5^{1-\frac{2}{3}\log_53+\frac{8}{3}\log_53}=5^{1+2\log_53}=5.5^{\log_53^2}=5.9=45\)
Ta có : \(C=\left(2^4.10^{-4}\right)^{-\frac{1}{4}}+3.64^{\frac{1}{12}}-\left(9-4\sqrt{2}\right)-7\sqrt{2}=5+3\sqrt{2}-9-3\sqrt{2}=-4\)
\(\frac{\left(\sqrt{5}-1\right)\left(6+2\sqrt{5}\right)}{\sqrt{5}-1}=\frac{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)^2}{\sqrt{5}-1}=4\)
\(A=\left(3\sqrt{3}\right)^{\frac{4}{3}}+\left(\frac{1}{16}\right)^{\frac{3}{4}}+2\left(\frac{8}{27}\right)^{\frac{2}{3}}\)
\(A=\left(3\sqrt{3}\right)^{\frac{4}{3}}+55+\frac{32}{3}\)
\(A=\left(3\sqrt{3}\right)^{\frac{4}{3}}+\frac{197}{3}\)
\(A=243+\frac{197}{3}\)
\(A=\frac{926}{3}\)
Ta có \(A=3^{\frac{3}{2}.\frac{4}{3}}+\left(\frac{1}{2}\right)^{4.\frac{3}{4}}+2\left(\frac{2}{3}\right)^{3.\frac{2}{3}}=3^2+\left(\frac{1}{2}\right)^3+2\left(\frac{2}{3}\right)^2=\frac{721}{72}\)
\(J=4^{1-2\log_2\sqrt[4]{7}}-36^{\log_62}+81^{0,25-0,5\log_97}=\left(2^2\right)^{1-2\log_2\sqrt[4]{7}}+\left(6^2\right)^{\log_62}+\left(3^4\right)^{0,25-\frac{1}{2}\log_{3^2}7}\)
\(=\frac{2^2}{2^{4\log_2\sqrt[4]{7}}}+6^{\log_64}+\frac{3}{3^{\log_37}}=\frac{4}{7}-4+\frac{3}{7}=-3\)