\(=\dfrac{5^2\cdot2^9\cdot3^9\cdot2\cdot5+2^5\cdot2^3\cdot3^5\cdot5^3\cdot3^3}{5^2\cdot2^8\cdot3^8\cdot2\cdot5-2\cdot2^8\cdot3^8\cdot2^3\cdot5^3}\)

\(=\dfrac{5^3\cdot2^{10}\cdot3^9+5^3\cdot2^8\cdot3^8}{5^3\cdot2^9\cdot3^8-5^3\cdot2^{12}\cdot3^8}\)

\(=\dfrac{5^3\cdot2^8\cdot3^8\left(2^2\cdot3+1\right)}{5^3\cdot2^9\cdot3^8\left(1-2^3\cdot1\right)}=\dfrac{1}{2}\cdot\dfrac{13}{1-9}=-\dfrac{13}{16}\)

Có: \(\dfrac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10}=\dfrac{5^2.2^9.3^9.2.5+2^5.3^5.2^3.3^3.5^3}{5^2.2^8.3^8.2.5-2.2^8.3^8.2^3.5^3}\)

=\(\dfrac{2^{10}.3^95^3+2^8.3^8.5^3}{2^9.3^8.5^3-2^{12}.3^8.5^3}=\dfrac{2^8.3^8.5^3.\left(12+1\right)}{2^8.3^8.5^3\left(2-16\right)}\)

= \(\dfrac{12+1}{2-16}=\dfrac{-13}{14}\)

= -14/13

\(\frac{5^2.6^9.10+6^5.2^3.15^3}{5^2.6^8.10-2.6^8.10^3}=\frac{5^2.2^9.3^9.2.5+2^5.3^5.2^3.5^3.3^3}{5^2.2^8.3^8.2.5-2.2^8.3^8.2^3.5^3}\)

\(=\frac{2^{10}.3^9.5^3+2^8.3^8.5^3}{2^9.3^8.5^3-2^{12}.3^8.5^3}=\frac{2^8.3^8.5^3\left(2^2.3+1\right)}{2^9.3^8.5^3\left(1-2^3\right)}\)

\(=\frac{13}{2.-7}=-\frac{13}{14}\)

\(1,\)

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

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

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

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

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

\(2,\)

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

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

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

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

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

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

\(3,\)

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

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

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

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

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

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

\(=1\)

\(4,\)

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

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

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

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

\(=-4\)

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

bài của Edo lag quá