\(=\dfrac{\left(2^3\right)^3.\left(3^2\right)^4-2^8.\left(3^4\right)^2}{\left(2^4\right)^2.\left(3^4\right)^2+\left(2^2\right)^4.\left(3^3\right)^3}=\dfrac{2^9.3^8-2^8.3^8}{2^8.3^8+2^8.3^9}=\)

\(=\dfrac{2^8.3^8.\left(2-1\right)}{2^8.3^8.\left(1+3\right)}=\dfrac{1}{4}\)

Ta có: \(\dfrac{4^7\cdot2^8}{3\cdot2^{15}\cdot16^2-5\cdot2^2\cdot\left(2^{10}\right)^2}\)

\(=\dfrac{2^{22}}{3\cdot2^{15}\cdot2^8-5\cdot2^2\cdot2^{20}}\)

\(=\dfrac{2^{22}}{2^{22}\left(3\cdot2-5\right)}\)

\(=1\)

\(\dfrac{3^{10}\cdot11+9^5\cdot5}{27^3\cdot2^4}\cdot x=-9\)

\(\dfrac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\cdot x=-9\)

\(\dfrac{3\cdot3^9\cdot16}{3^9\cdot16}\cdot x=-9\)

3x = -9

\(x=-\dfrac{9}{3}=-3\)

\(\dfrac{3\cdot3^9\cdot\left(11+5\right)}{3^9\cdot16}\cdot x=-9\)

  \(\frac{27^3+9^{10}.2^4+4^2.81^5}{3^{10}+3^{21}.2^5}\)

=\(\frac{3^9+3^{20}.2^4+2^4.3^{20}}{3^{10}+3^{21}.2^5}\)

=\(\frac{3^{18}+2^3}{1}\)

= \(3^{18}+2^3\)

Hk tốt

\(B=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\)

\(B=\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+3^{10}.2^{20}}\)

\(B=\frac{2^{19}.3^9+3^9.5.2^{18}}{2^{19}.3^9+3^{10}.2^{20}}\)

\(B=\frac{2^{18}.3^9.\left(2+5\right)}{2^{19}.3^9\left(1+3.2\right)}\)

\(B=\frac{7}{2.7}\)

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

\(C=\frac{2^{13}.4^{11}-16^9}{\left(3.2^{17}\right)^2}\)

\(C=\frac{2^{13}.2^{22}-2^{36}}{3^2.2^{34}}\)

\(C=\frac{2^{35}-2^{36}}{3^2.2^{34}}\)

\(C=\frac{2^{35}\left(1-2\right)}{3^2.2^{34}}\)

\(C=\frac{-2}{9}\)

\(D=\frac{4^7.2^8}{3.2^{15}.16^2-5.2^2.\left(2^{10}\right)^2}\)

\(D=\frac{2^{14}.2^8}{3.2^{15}.2^8-5.2^2.2^{20}}\)

\(D=\frac{2^{14}.2^8}{3.2^{23}-5.2^{22}}\)

\(D=\frac{2^{22}}{2^{22}\left(3.2-5\right)}\)

\(D=1\)

\(A=\dfrac{12^{15}\cdot3^4-4^5\cdot3^9}{27^3\cdot2^{10}-32^3\cdot3^9}\\ =\dfrac{\left(2^2\cdot3\right)^{15}\cdot3^4-\left(2^2\right)^5\cdot3^9}{\left(3^3\right)^3\cdot2^{10}-\left(2^5\right)^3\cdot3^9}\\ =\dfrac{2^{30}\cdot3^{15}\cdot3^4-2^{10}\cdot3^9}{3^9\cdot2^{10}-2^{15}\cdot3^9}\\ =\dfrac{3^9\cdot2^{10}\left(2^{20}\cdot3^{10}\right)}{3^9\cdot2^{10}\left(1-2^5\right)}\\ =\dfrac{\left(2^2\right)^{10}\cdot3^{10}}{1-32}\\ =\dfrac{\left(2^2\cdot3\right)^{10}}{-31}\\ =\dfrac{-12^{10}}{31}\)

\(B=\dfrac{3}{1^2\cdot2^2}+\dfrac{5}{2^2\cdot3^2}+...+\dfrac{99}{49^2\cdot50^2}\\ =\dfrac{2^2-1^2}{1^2\cdot2^2}+\dfrac{3^2-2^2}{2^2\cdot3^2}+...+\dfrac{50^2-49^2}{49^2\cdot50^2}\\ =\dfrac{1}{1^2}-\dfrac{1}{2^2}+\dfrac{1}{2^2}-\dfrac{1}{3^2}+...+\dfrac{1}{49^2}-\dfrac{1}{50^2}\\ =1-\dfrac{1}{2500}\\ =\dfrac{2499}{2500}\)

\(B=\dfrac{3^6\cdot3^3\cdot5^3+3^6\cdot3^6\cdot5^6}{3^{10}\cdot5^3\cdot2^3}=\dfrac{3^9\cdot5^3\left(1+3^3\cdot5^3\right)}{3^{10}\cdot5^3\cdot2^3}=\dfrac{1+15^3}{3\cdot2^3}=\dfrac{3376}{24}=\dfrac{422}{3}\)

\(1,\)

\(\dfrac{45^2.3^8.10^5}{5^5.3^7.18^5}\)

\(=\dfrac{3^4.5^2.3^8.2^5.5^5}{5^5.3^7.2^5.3^{10}}\)

\(=\dfrac{3^{12}.2^5.5^7}{5^5.3^{17}.2^5}\)

\(=\dfrac{1.5^2}{3^5.1}\)

\(=\dfrac{25}{243}\)

\(2,\)

\(\dfrac{4^5.9^4+2.6^9}{2^{10}.3^8+6^8.20}\)

\(=\dfrac{2^{10}.3^8+2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)

\(=\dfrac{2^{10}.3^8+2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)

\(=\dfrac{2^{10}.3^8.4}{2^{10}.3^8.6}\)

\(=\dfrac{2^{12}.3^8}{2^{11}.3^9}\)

\(=\dfrac{2}{3}\)

\(3,\)

\(\dfrac{15.3^{11}+4.27^4}{9^7}\)

\(=\dfrac{3.5.3^{11}+2^2.3^{12}}{3^{14}}\)

\(=\dfrac{5.3^{12}+2^2.3^{12}}{3^{14}}\)

\(=\dfrac{3^{12}\left(5+2^2\right)}{3^{14}}\)

\(=\dfrac{3^{12}.9}{3^{14}}\)

\(=\dfrac{3^{14}}{3^{14}}\)

\(=1\)

\(4,\)

\(\dfrac{4^7.2^8}{3.2^{15}.16^2-5^2\left(2^{10}\right)^2}\)

\(=\dfrac{2^{22}}{3.2^{23}-5^2.2^{20}}\)

\(=\dfrac{2^{22}}{2^{20}.\left(-1\right)}\)

\(=\dfrac{2^{22}}{-2^{20}}\)

\(=-4\)

* Mấy bài còn lại tương tự đấy bạn tự làm đi

Mình mỏi tay lắm rồi

P/s:khuyến khích tự làm,chỉ làm mẫu 1 câu:

1)\(\dfrac{45^2.3^8.10^5}{5^5.3^7.18^5}=\dfrac{\left(5.9\right)^2.3.3^7.\left(2.5\right)^5}{5^5.3^7.\left(2.9\right)^5}\)\(=\dfrac{5^2.9^2.3.3^7.2^5.5^5}{5^5.3^7.2^5.9^5}\)\(=\dfrac{5^2.9^2.3.1.1.1}{1.1.1.9^5}\)\(=\dfrac{5^2.9^2.3}{9^5}=\dfrac{5^2.9^2.3}{9^2.9^3}=\dfrac{5^2.3}{9^3}=\dfrac{75}{729}=\dfrac{25}{243}\)

1) \(\dfrac{1}{4}x-\dfrac{1}{3}=\dfrac{-5}{9}\)

\(\Rightarrow\dfrac{1}{4}x=-\dfrac{2}{9}\Rightarrow x=-\dfrac{8}{9}\)

2) \(2^{x-3}-3.2^x=-92\)

\(\Rightarrow2^x\left(2^{-3}-3\right)=-92\)

\(\Rightarrow2^x.\dfrac{-23}{9}=-92\)

\(\Rightarrow2^x=32\Rightarrow x=5\)