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\(4.\left(\frac{1}{4}\right)^2+25\left[\left(\frac{3}{4}\right)^3:\left(\frac{5}{4}\right)^3\right]:\left(\frac{3}{2}\right)^3=4.\frac{1}{16}+25\left(\frac{27}{64}.\frac{64}{125}\right).\frac{8}{27}\)
\(=\frac{1}{4}+25.\frac{27}{125}.\frac{8}{27}=\frac{1}{4}+\frac{8}{5}=\frac{37}{20}\)
\(2^3+3\left(\frac{1}{2}\right)^0-1+\left[\left(-2\right)^2:\frac{1}{2}\right]-8=8+3-1+4.2-8=10\)
a) \(C=\frac{\left(\frac{2}{3}\right)^3\times\left(-\frac{3}{4}\right)^2\times\left(-1\right)^5}{\left(\frac{2}{5}\right)^2\times\left(-\frac{5}{12}\right)^2}\)
\(C=\frac{\frac{2^3}{3^3}.\frac{\left(-3\right)^2}{4^2}.\left(-1\right)^5}{\frac{2^2}{5^2}.\frac{\left(-5\right)^2}{12^2}}\)
\(C=\frac{\frac{-\left(2^3.3^2\right)}{3^3.2^4}}{\frac{2^2.5^2}{5^2.2^4.3^2}}\)
\(C=\frac{\frac{-1}{3.2}}{\frac{1}{2^2.3^2}}\)
\(C=\frac{\frac{-1}{6}}{\frac{1}{36}}\)
\(C=-6\)
b) \(D=\frac{6^6+6^3\times3^3+3^6}{-73}\)
\(D=\frac{2^6.3^6+2^3.3^3.3^3+3^6}{-73}\)
\(D=\frac{2^6.3^6+2^3.3^6+3^6}{-73}\)
\(D=\frac{3^6\left(2^6+2^3+1\right)}{-73}\)
\(D=\frac{3^6.73}{\left(-1\right).73}\)
\(D=-3^6=-729\)
Dễ thấy 6,3 . 12 - 21 . 3,6 = 63 . 1,2 - 63 . 1,2 = 0
Do đó biểu thức trên bằng 0
\(A=\left(2-\frac{3}{2}\right).\left(2-\frac{4}{3}\right).\left(2-\frac{5}{4}\right).\left(2-\frac{6}{5}\right)\)
\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}\)
\(A=\frac{1}{5}\)
\(A=\left(2-\frac{3}{2}\right)\times\left(2-\frac{4}{3}\right)\times\left(2-\frac{5}{4}\right)\times\left(2-\frac{6}{5}\right)\)
\(\Rightarrow\)\(A=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\)
\(\Rightarrow A=\frac{1}{5}\)
\(=\frac{11}{-5}\cdot\frac{-9}{11}\cdot\frac{15}{-14}\cdot\frac{2}{5}+-\frac{2}{77}\cdot\frac{5}{-3}\)
\(=\frac{9}{5}\cdot-\frac{15}{14}\cdot\frac{2}{5}+\frac{10}{231}\)
\(=-\frac{841}{1155}\)
\(\left|\frac{-2}{3}+\frac{3}{2}\right|.\left(\frac{-4}{5}-\left|-\frac{3}{-2}-1\right|\right)\)
\(=\left|\frac{5}{6}\right|.\left(\frac{-4}{5}-\left|\frac{1}{2}\right|\right)\)
\(=\frac{5}{6}.\left(\frac{-4}{5}-\frac{1}{2}\right)\)
\(=\frac{5}{6}.\frac{-13}{10}\)
\(=\frac{-13}{12}\)
\(\left|\frac{-2}{3}+\frac{3}{2}\right|.\left(\frac{-4}{5}-\left|-\frac{-3}{2}-1\right|\right)\)
\(=\left|\frac{-4}{6}+\frac{9}{6}\right|.\left(\frac{-4}{5}-\left|\frac{3}{2}-1\right|\right)\)
\(=\left|\frac{5}{6}\right|.\left(\frac{-4}{5}-\left|\frac{3}{2}-\frac{2}{2}\right|\right)\)
\(=\frac{5}{6}.\left(\frac{-4}{5}-\left|\frac{1}{2}\right|\right)\)
\(=\frac{5}{6}.\left(\frac{-4}{5}-\frac{1}{2}\right)\)
\(=\frac{5}{6}.\left(\frac{-8}{10}-\frac{5}{10}\right)\)
\(=\frac{5}{6}.\frac{-13}{10}\)
\(=\frac{5.\left(-13\right)}{6.10}=\frac{-13}{6.2}=\frac{-13}{12}=-1\frac{1}{12}\)
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