\(\frac{4^8.3^{12}.27^2}{6^{12}.9^3}\)

= \(\frac{\left(2^2\right)^8.3^{12}.27^2}{\left(2.3\right)^{12}.\left(3^2\right)^3}\)

= \(\frac{2^{16}.3^{12}.27^2}{2^{12}.3^{12}.27^2}\)

= \(\frac{2^{16}}{2^{12}}\)= 2⁴ = 16

\(8\frac{4}{17}-\left(2\frac{5}{9}+3\frac{4}{17}\right)=\frac{140}{17}-\left(\frac{23}{9}+\frac{55}{17}\right)=\frac{140}{17}-\frac{886}{153}=\frac{22}{9}=2,444444444444\)

=[ 15+1.27-2³]:(-17)

=[15+1.27-8]:(-17)

=[15+27-8]:(-17)

=[42-8]:(-17)

=34:(-17)

=-2

=[15+ ( -1) . 27 - 8] : (-17)

= [15 + (-27) - 8] : ( -17)

= [ -12 - 8] : (-17)

= -20 : (-17)

= 1.17647058824

=>3^x(1+3^2)=3^34+3^36

=>3^x.10=3^34.10

=>3^x=3^34

=>x=34

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

\(=\frac{5.2^{30}.3^{18}-2^{29}.3^{20}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\)

\(=\frac{2^{29}.3^{18}.1}{2^{28}.3^{18}.1}\)

\(=2\)

\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)

\(=\frac{5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9}{5.2^9.2^{19}.3^{19}-7.2^{29}.\left(3^3\right)^6}\)

\(=\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

\(=\frac{5.2^{29}.2.3^{18}-2^{29}.3^{18}.3^2}{5.2^{28}.3^{18}.3-7.2^{28}.2.3^{18}}\)

\(=\frac{2^{29}.3^{18}.\left(5.2-3^2\right)}{2^{28}.3^{18}.\left(5.3-7.2\right)}\)

\(=\frac{2^{29}.3^{18}.\left(10-9\right)}{2^{28}.3^{18}.\left(15-14\right)}\)

\(=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}\)

\(=\frac{2^{28}.2.3^{18}}{2^{28}.3^{18}}\)

\(=2\)

\(\left(15.3^{42}-9^{20}\right):27^3\)

\(=\left(5.3.3^{42}-3^{40}\right):3^9\)

\(=\left(5.3^{43}-3^{40}\right):3^9\)

\(=3^{40}\left(5.3^3-1\right):3^9\)

\(=3^{31}\left(5.3^3-1\right)\)

\(=134.3^{31}\)

\(\left(15.3^{42}-9^{20}\right):27^3=15.3^{42}:27^3-9^{20}:27^3\\ \\ =15.3^{42}:\left(3^3\right)^3-9^{20}:9^3:3^3=15.3^{33}-\left(3^2\right)^{20}:\left(3^2\right)^3:3^3\)

\(=15.3^{33}-3^{40}:3^6:3^3=15.3^{33}-3^{31}\\ \\ =15.3^2.3^{31}-3^{31}=135.3^{31}-3^{31}\\ \\ =3^{31}.\left(135-1\right)=3^{31}.134\)

A) \(\frac{1}{2}\cdot\left(\frac{2}{9}+\frac{3}{7}-\frac{5}{27}\right)\) 

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

\(=\frac{1}{4}\)

B)   \(\left(\frac{-5}{28}+1.75+\frac{8}{35}\right):\left(-3\frac{9}{20}\right)\)

\(=\left(\frac{-5}{28}+\frac{7}{4}+\frac{8}{35}\right):\frac{-69}{20}\)

\(=\frac{14}{5}:\frac{-69}{20}\)

\(=\frac{-56}{69}\)

Ta có:\(\frac{5.4^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)=\(\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}}\)=\(\frac{5.2^{30}.3^{18}-2^2.3^{20}.2^{27}}{5.2^{28}.3^{19}-7.2^{29}.3^{18}}\)

=\(\frac{2^{29}.3^{18}.(5.2-9)}{2^{28}.3^{18}.(5.3-7.2)}\)=\(\frac{2^{29}.3^{18}.1}{2^{28}.3^{18}.1}\)=\(\frac{2}{1}\)= 2