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A. 2.9 +6 -4 = 20
B. 8.25 - 6.9 + (-12) = 134
C. -962 + 1548 = 586
D. -85.(36+54) = -85 x 100 = -8500
F. 26.37 - 26.56 - 56.37 + 56.26 =26.37 - 56.37 = 37.(26 - 56)
=37. (-30) = -1100
E. 130 - ( 27 - (36 + 128).2))3
= 130 - ( 27 - 328).3
= 130 - (-301).3
= 130 - (-903)
= 1033
\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.234.8^2}=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.3^5.\left(2^3\right)^2}\)
\(M=\frac{3^8.3^{15}.3^6.3^4}{3^{18}.3^{16}.3^5.2^6}=\frac{81}{64}\)
\(N=\frac{4^6.9^5.6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(N=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2.6}{3.5}\)
\(N=\frac{4}{5}\)
\(\dfrac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}\) \(=\dfrac{7.\left(2^2\right)^5+2^{13}.\left(3^3\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}\) \(=\dfrac{7.2^{10}.3^{11}+2^{13}.3^{15}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\dfrac{7.2^{10}.3^{10}.3+2^{10}.2^3.3^{10}.3^5}{2^{10}.3^{10}+2^{10}.2^2.3^{10}}\) \(=\dfrac{2^{10}.3^{10}\left(7.3+2^3.3^5\right)}{2^{10}.3^{10}\left(1+2^2\right)}\)
\(=\dfrac{7.3+2^3.3^5}{1+2^2}\) \(=\dfrac{21+8.243}{5}\) \(=\dfrac{1965}{5}=393\)
\(\dfrac{7.4^5.3^{11}+2^{13}.9^5}{6^{11}+2^{12}.3^{10}}\)=\(\dfrac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{11}+2^{12}.3^{11}}\)=\(\dfrac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{11}.3^{11}+2^{12}.3^{11}}\)
= \(\dfrac{3^{10}.\left(7.3.2^{10}+2^{13}\right)}{3^{11}.\left(2^{11}+2^{12}\right)}\)=\(\dfrac{3^{10}.\left(21.2^{10}+2^{13}\right)}{3^{11}.\left(2^{11}+2^{12}\right)}\)=\(\dfrac{21.2^{10}+2^{13}}{3.\left(2^{11}+2^{12}\right)}\)
\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\frac{2^{10}.3^{10}.\left(7.3+2^3\right)}{2^{10}.3^{10}.\left(1+2^2\right)}=\frac{7.3+2^3}{1+2^2}=\frac{29}{5}\)