a) \(A=\dfrac{12^3\cdot54^2}{108^4}\)
\(=\dfrac{12^3\cdot2^2\cdot\left(3^3\right)^2}{9^4\cdot12^4}\)
\(=\dfrac{4\cdot3^6}{\left(3^2\right)^4\cdot12}\)
\(=\dfrac{1\cdot3^5}{3^8}\)
\(=\dfrac{1}{3^3}\)
\(=\dfrac{1}{27}\)
b) \(B=\dfrac{3^{12}\cdot13+3^{12}\cdot3}{3^{11}\cdot2^4}\)
\(=\dfrac{13\cdot3^{12}+3\cdot3^{12}}{3^{11}\cdot2^4}\)
\(=\dfrac{16\cdot3^{12}}{3^{11}\cdot2^4}\)
\(=\dfrac{2^4\cdot3}{2^4}\)
\(=3\)
c) \(C=\dfrac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}\)
\(=\dfrac{13\cdot2^{10}+65\cdot2^{10}}{2^8\cdot104}\)
\(=\dfrac{78\cdot2^{10}}{2^8\cdot104}\)
\(=\dfrac{3\cdot2^2}{4}\)
\(=\dfrac{3\cdot4}{4}\)
\(=3\)
\(B=\dfrac{3^{12}.13+3^{12}.3}{3^{11}.2^4}=\dfrac{3^{12}.\left(13+3\right)}{3^{11}.16}=\dfrac{3^{12}.16}{3^{11}.16}=3\)
\(C=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}=\dfrac{2^{10}.\left(13+65\right)}{2^8.104}=\dfrac{4.78}{104}=\dfrac{3}{101}\)
d) \(D=\dfrac{8^{10}+4^{10}}{8^4+4^{11}}\)
\(=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}\)
\(=\dfrac{\left(2^{10}+1\right)\cdot2^{20}}{\left(1+2^{10}\right)\cdot2^{12}}\)
\(=\dfrac{\left(1024+1\right)\cdot2^8}{1+1024}\)
\(=\dfrac{1025\cdot2^8}{1025}\)
\(=2^8\)
\(=256\)
e) \(E=\dfrac{30\cdot4^7\cdot3^{29}-5\cdot14^5\cdot2^{12}}{54\cdot6^{14}\cdot9^7-12\cdot8^5\cdot7^5}\)
\(=\dfrac{5\cdot3\cdot2\cdot2^{14}\cdot3^{29}-5\cdot14^5\cdot4096}{9\cdot6\cdot6^{14}\cdot9^7-3\cdot2^2\cdot2^{15}\cdot7^5}\)
\(=\dfrac{5\cdot3^{30}\cdot2^{15}-20480\cdot14^5}{9^8\cdot6^{15}-3\cdot2^{17}\cdot7^5}\)
\(=\dfrac{5\cdot3^{30}\cdot32768-20480\cdot14^5}{9^8\cdot6^{15}-3\cdot2^{17}\cdot16807}\)
\(=\dfrac{163840\cdot3^{30}-20480\cdot14^5}{9^8\cdot6^{15}-50421\cdot2^{17}}\)
f) \(F=\dfrac{16^3\cdot3^{16}+120\cdot6^9}{4^6\cdot3^{12}+6^{11}}\)
\(=\dfrac{2^{12}\cdot3^{16}+20\cdot6\cdot6^9}{2^{12}\cdot3^{12}+6^{11}}\)
\(=\dfrac{3^4\cdot6^{12}+20\cdot6^{10}}{\left(2\cdot3\right)^{12}+6^{11}}\)
\(=\dfrac{81\cdot6^{12}+20\cdot6^{10}}{6^{12}+6^{11}}\)
\(=\dfrac{\left(81\cdot6^2+20\right)\cdot6^{10}}{\left(6+1\right)\cdot6^{11}}\)
\(=\dfrac{81\cdot36+20}{7\cdot6}\)
\(=\dfrac{2916+20}{7\cdot6}\)
\(=\dfrac{2936}{7\cdot6}\)
\(=\dfrac{1468}{7\cdot3}\)
\(=\dfrac{1468}{21}\)
a) \(\dfrac{72^3.54^2}{108^4}\)
\(=\dfrac{2^9.3^6.2^2.3^2.3^4}{\left(2^2.3^3\right)^4}\)
\(=\dfrac{2^8.2.3^{12}}{2^8.3^{12}}=2\)
\(D=\dfrac{8^{10}+4^{10}}{8^4+4^{11}}\)
\(D=\dfrac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}\)
\(D=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=\dfrac{2^{20}}{2^{12}}=2^8=256\)
P/s :Biết làm mỗi câu này thông cảm nha
6.30 túi là tớ đi học rùi.cứu tớ nhé.huhu