\(4.\left(\frac{1}{4}\right)^2+25\left[\left(\frac{3}{4}\right)^3:\left(\frac{5}{4}\right)^3\right]:\left(\frac{3}{2}\right)^3=4.\frac{1}{16}+25\left(\frac{27}{64}.\frac{64}{125}\right).\frac{8}{27}\)

\(=\frac{1}{4}+25.\frac{27}{125}.\frac{8}{27}=\frac{1}{4}+\frac{8}{5}=\frac{37}{20}\)

\(2^3+3\left(\frac{1}{2}\right)^0-1+\left[\left(-2\right)^2:\frac{1}{2}\right]-8=8+3-1+4.2-8=10\)

\(A=2\frac{1}{2}\)

\(A=\left(2-\frac{3}{2}\right).\left(2-\frac{4}{3}\right).\left(2-\frac{5}{4}\right).\left(2-\frac{6}{5}\right)\)

\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}\)

\(A=\frac{1}{5}\)

\(A=\left(2-\frac{3}{2}\right)\times\left(2-\frac{4}{3}\right)\times\left(2-\frac{5}{4}\right)\times\left(2-\frac{6}{5}\right)\)

\(\Rightarrow\)\(A=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\)

\(\Rightarrow A=\frac{1}{5}\)

\(A=\left(2-\dfrac{3}{2}\right)\left(2-\dfrac{4}{3}\right)\left(2-\dfrac{5}{4}\right)\left(2-\dfrac{6}{5}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5}\)

\(=\dfrac{1}{5}\)

-20/147

=\(\frac{-4}{15}\)

\(\frac{\left(\frac{1}{14}-\frac{\sqrt{2}}{7}+\frac{3\sqrt{2}}{35}\right)\cdot\left(\frac{-4}{15}\right)}{\left(\frac{1}{10}+\frac{3\sqrt{2}}{25}-\frac{\sqrt{2}}{5}\right)\cdot\frac{5}{7}}\)

\(=-\frac{\left(\frac{1}{14}-\frac{\sqrt{2}}{7}+\frac{3\sqrt{2}}{35}\right)\cdot\frac{4}{15}}{\left(\frac{1}{10}+\frac{3\sqrt{2}}{25}-\frac{\sqrt{2}}{5}\right)\cdot\frac{5}{7}}\)

\(=-\frac{\frac{4}{15}\cdot\frac{5-4\sqrt{2}}{70}}{\frac{5}{7}\cdot\frac{5-4\sqrt{2}}{50}}\)

\(=-\frac{4\left(5-4\sqrt{2}\right)}{15\left(5-4\sqrt{2}\right)}\)

\(=-\frac{4}{15}\)

A = (4+\(\frac{1}{5}\)) . \(\frac{18}{19}\)+ (2+\(\frac{8}{5}\)) . \(\frac{21}{5}\)

A= \(\frac{21}{5}\).18/19 + 18/5 . 21/5

A= 21/5 (18/19 + 18/5)

A= 21/5 . 432/95

A= 9288/95

b= 25/2. (3+2/7) - 23/7. (5 + 1/2)

b= 25/2 . 23/7 - 23/7 . 11/2

b= 23/7 (25/2 -11/2)

b=23/7 . 7

b= 23

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) \(D=\frac{6^6+6^3\times3^3+3^6}{-73}\)

\(D=\frac{2^6.3^6+2^3.3^3.3^3+3^6}{-73}\)

\(D=\frac{2^6.3^6+2^3.3^6+3^6}{-73}\)

\(D=\frac{3^6\left(2^6+2^3+1\right)}{-73}\)

\(D=\frac{3^6.73}{\left(-1\right).73}\)

\(D=-3^6=-729\)

\(=\frac{11}{-5}\cdot\frac{-9}{11}\cdot\frac{15}{-14}\cdot\frac{2}{5}+-\frac{2}{77}\cdot\frac{5}{-3}\)
\(=\frac{9}{5}\cdot-\frac{15}{14}\cdot\frac{2}{5}+\frac{10}{231}\)
\(=-\frac{841}{1155}\)