\(C=\dfrac{2^6\cdot3^{10}}{3^9\cdot2^6}=3\\ D=\dfrac{3^{24}\cdot3^{10}}{3^{21}\cdot3^{11}}=\dfrac{3^{34}}{3^{32}}=3^2=9\\ F=\dfrac{2^{45}\cdot5^{14}}{5^{15}\cdot2^{47}}=\dfrac{1}{2^2\cdot5}=\dfrac{1}{20}\\ G=\dfrac{2^2\cdot5^2\cdot5^3}{2^3\cdot5^4}=\dfrac{1\cdot5}{2}=\dfrac{5}{2}\)

C=3

D=9

F=1/20

G=5/2

Em ko giải chi tiết vì nó lâu

Mong thông cảm!

C= \(\dfrac{8^2.9^5}{3^9.4^3}\)

   = \(\dfrac{\left(2^3\right)^2.\left(3^2\right)^5}{3^9.\left(2^2\right)^3}\)

   = \(\dfrac{2^6.3^{10}}{3^9.2^6}\)

   = \(\dfrac{3^1}{1}\)

   = \(\dfrac{3}{1}\)

\(\dfrac{8^{14}}{4^4.64^5}=\dfrac{\left(2^3\right)^{14}}{\left(2^2\right)^4.\left(2^5\right)^5}=\dfrac{2^{42}}{2^8.2^{25}}=2^{42-\left(8+25\right)}=2^9\)

\(\dfrac{9^{10}.27^7}{81^7.3^{15}}=\dfrac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}=\dfrac{3^{20}.3^{21}}{3^{28}.3^{15}}=\dfrac{3^{20+21}}{3^{28+15}}=\dfrac{3^{41}}{3^{41}.3^2}=\dfrac{1}{3^2}=\dfrac{1}{9}\)

a: \(A=\dfrac{5^2\cdot3^{11}\cdot2^{11}\cdot2^8+3^2\cdot2^2\cdot2^{12}\cdot3^6\cdot3^2\cdot5^2}{2\cdot2^{12}\cdot3^{12}\cdot2^4\cdot5^4-3^8\cdot960^3}\)

\(=\dfrac{5^2\cdot3^{11}\cdot2^{19}+3^{10}\cdot2^{14}\cdot5^2}{2^{17}\cdot3^{12}\cdot5^4-3^{11}\cdot2^{18}\cdot5^3}\)

\(=\dfrac{5^2\cdot2^{14}\cdot3^{10}\left(3\cdot2^5+1\right)}{2^{17}\cdot3^{11}\cdot5^3\left(3\cdot5-2\right)}=\dfrac{1}{5}\cdot\dfrac{1}{8}\cdot\dfrac{1}{10}\cdot\dfrac{97}{13}=\dfrac{97}{5200}\)

b: \(B=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)

\(=\dfrac{-2^{12}\cdot3^{10}-2^{12}\cdot3^{10}\cdot5}{-2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot7}=\dfrac{2\cdot6}{3\cdot7}=\dfrac{12}{21}=\dfrac{4}{7}\)

a) \(\frac{9^{10}.27^7}{81^7.3^{15}}\)= \(\frac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}\)= \(\frac{3^{2.10}.3^{3.7}}{3^{4.7}.3^{15}}\)=\(\frac{3^{20}.3^{21}}{3^{28}.3^{15}}\)=\(\frac{3^{41}}{3^{43}}\)= \(\frac{3^{41}}{3^{41}.3^2}\)= \(\frac{1}{3^2}=\frac{1}{9}\)

b) \(\frac{8^3.9^5.27^5}{4^5.81^6}\)= \(\frac{\left(2^3\right)^3.\left(3^2\right)^5.\left(3^3\right)^5}{\left(2^2\right)^5.\left(3^4\right)^6}\)= \(\frac{2^{3.3}.3^{2.5}.3^{3.5}}{2^{2.5}.3^{4.6}}\)=\(\frac{2^9.3^{10}.3^{15}}{2^{10}.3^{24}}\)= \(\frac{2^9.3^{25}}{2^{10}.3^{24}}\)=\(\frac{2^9.3^{24}.3}{2^9.2.3^{24}}\)=\(\frac{3}{2}\)

\(=\dfrac{5^3\left(2^3+2+1\right)}{55}-\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)

\(=5^2-\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=25-\dfrac{2}{3}\cdot\dfrac{6}{5}\)

=25-4/5

=24,2

\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}=\dfrac{2.6}{3.5}=\dfrac{4}{5}\)

Giải giúp em với mn

\(A=\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5+6^9.6.2^2.5}{\left(2^3\right)^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\dfrac{2^{11}.3^{10}\left(2^1+2^1.5\right)}{2^{11}.3^{10}\left(2^1.3^2-1.3^1\right)}=\dfrac{2+10}{2.9-1.3}=\dfrac{12}{15}=\dfrac{4}{5}\)