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\(4.\left(\frac{1}{4}\right)^2+25\left[\left(\frac{3}{4}\right)^3:\left(\frac{5}{4}\right)^3\right]:\left(\frac{3}{2}\right)^3=4.\frac{1}{16}+25\left(\frac{27}{64}.\frac{64}{125}\right).\frac{8}{27}\)
\(=\frac{1}{4}+25.\frac{27}{125}.\frac{8}{27}=\frac{1}{4}+\frac{8}{5}=\frac{37}{20}\)
\(2^3+3\left(\frac{1}{2}\right)^0-1+\left[\left(-2\right)^2:\frac{1}{2}\right]-8=8+3-1+4.2-8=10\)
\(=\left(\frac{1}{2}+\frac{1}{3}\right):\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{2}.1\right):2^3\)
\(=\frac{5}{6}:\frac{1}{6}+\frac{1}{2}:8\)
\(=5+\frac{1}{16}\)
\(=\frac{81}{16}\)
+) \(40\div\left\{\left[11+\left(26-27\right)\right]\times2\right\}\)
\(=40\div\left(10\times2\right)=2\)
+) \(\left|\frac{3}{5}\right|\times4\frac{1}{7}+\left|\frac{-6}{7}\right|\times\frac{3}{5}\)
\(=\frac{3}{5}\times\frac{29}{7}+\frac{6}{7}\times\frac{3}{5}=\frac{3}{5}\times\left(\frac{29}{7}+\frac{6}{7}\right)=\frac{3}{5}\times5=3\)
\(=\frac{11}{-5}\cdot\frac{-9}{11}\cdot\frac{15}{-14}\cdot\frac{2}{5}+-\frac{2}{77}\cdot\frac{5}{-3}\)
\(=\frac{9}{5}\cdot-\frac{15}{14}\cdot\frac{2}{5}+\frac{10}{231}\)
\(=-\frac{841}{1155}\)
a,
\(\dfrac{\left(3^3\right)^{15}.5^3.\left(2^3\right)^4}{\left(5^2\right)^2.\left(3^4\right)^{11}.2^{11}}=\dfrac{3^{45}.5^3.2^{12}}{5^4.3^{44}.2^{11}}=\dfrac{6}{5}\)
b, \(\left(-\dfrac{14}{25}\right)^2.\dfrac{125}{49}+\left(-3\dfrac{11}{36}\right).2\dfrac{2}{17}=\dfrac{4}{5}.\left(-7\right)=-\dfrac{28}{5}\)
c, \(\dfrac{1}{3}-2.1=-\dfrac{5}{3}\)
\(=\left(4\times2^5\right):\left(\frac{8.1}{16}\right)=128:\frac{1}{2}=256\)