Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(1,\)
\(\dfrac{45^2.3^8.10^5}{5^5.3^7.18^5}\)
\(=\dfrac{3^4.5^2.3^8.2^5.5^5}{5^5.3^7.2^5.3^{10}}\)
\(=\dfrac{3^{12}.2^5.5^7}{5^5.3^{17}.2^5}\)
\(=\dfrac{1.5^2}{3^5.1}\)
\(=\dfrac{25}{243}\)
\(2,\)
\(\dfrac{4^5.9^4+2.6^9}{2^{10}.3^8+6^8.20}\)
\(=\dfrac{2^{10}.3^8+2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)
\(=\dfrac{2^{10}.3^8+2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(=\dfrac{2^{10}.3^8.4}{2^{10}.3^8.6}\)
\(=\dfrac{2^{12}.3^8}{2^{11}.3^9}\)
\(=\dfrac{2}{3}\)
\(3,\)
\(\dfrac{15.3^{11}+4.27^4}{9^7}\)
\(=\dfrac{3.5.3^{11}+2^2.3^{12}}{3^{14}}\)
\(=\dfrac{5.3^{12}+2^2.3^{12}}{3^{14}}\)
\(=\dfrac{3^{12}\left(5+2^2\right)}{3^{14}}\)
\(=\dfrac{3^{12}.9}{3^{14}}\)
\(=\dfrac{3^{14}}{3^{14}}\)
\(=1\)
\(4,\)
\(\dfrac{4^7.2^8}{3.2^{15}.16^2-5^2\left(2^{10}\right)^2}\)
\(=\dfrac{2^{22}}{3.2^{23}-5^2.2^{20}}\)
\(=\dfrac{2^{22}}{2^{20}.\left(-1\right)}\)
\(=\dfrac{2^{22}}{-2^{20}}\)
\(=-4\)
* 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) \(\frac{3^{10}+6^2}{5\cdot3^8+20}=\frac{3^{10}+3^2\cdot2^2}{5\cdot3^8+5\cdot2^2}=\frac{3^2\left(3^8+2^2\right)}{5\left(3^8+2^2\right)}=\frac{9}{5}\)
2) \(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{28^{15}\cdot3^{17}}{28^{16}\cdot3^{16}}=\frac{3}{28}\)
\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\frac{2^{10}.3^{10}.\left(7.3+2^3\right)}{2^{10}.3^{10}.\left(1+2^2\right)}=\frac{7.3+2^3}{1+2^2}=\frac{29}{5}\)
\(\dfrac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}\) \(=\dfrac{7.\left(2^2\right)^5+2^{13}.\left(3^3\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}\) \(=\dfrac{7.2^{10}.3^{11}+2^{13}.3^{15}}{2^{10}.3^{10}+2^{12}.3^{10}}\)
\(=\dfrac{7.2^{10}.3^{10}.3+2^{10}.2^3.3^{10}.3^5}{2^{10}.3^{10}+2^{10}.2^2.3^{10}}\) \(=\dfrac{2^{10}.3^{10}\left(7.3+2^3.3^5\right)}{2^{10}.3^{10}\left(1+2^2\right)}\)
\(=\dfrac{7.3+2^3.3^5}{1+2^2}\) \(=\dfrac{21+8.243}{5}\) \(=\dfrac{1965}{5}=393\)
\(\dfrac{7.4^5.3^{11}+2^{13}.9^5}{6^{11}+2^{12}.3^{10}}\)=\(\dfrac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{11}+2^{12}.3^{11}}\)=\(\dfrac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{11}.3^{11}+2^{12}.3^{11}}\)
= \(\dfrac{3^{10}.\left(7.3.2^{10}+2^{13}\right)}{3^{11}.\left(2^{11}+2^{12}\right)}\)=\(\dfrac{3^{10}.\left(21.2^{10}+2^{13}\right)}{3^{11}.\left(2^{11}+2^{12}\right)}\)=\(\dfrac{21.2^{10}+2^{13}}{3.\left(2^{11}+2^{12}\right)}\)
\(A=\frac{8^{10}+4^{10}}{8^4+4^{11}}\\ =\frac{8^4.8^6+4^{10}}{8^4+4^{10}.4}\\ =\frac{8^6}{4}\\ =\frac{262144}{4}\\ =65536\)
Lời giải:
Gọi biểu thức là $A$
\(A=\frac{2^{10}.3^8+5.(2^2)^5.3^8}{2^{10}.(3^3)^3-2^{10}.(3^2)^4}=\frac{2^{10}.3^8+5.2^{10}.3^8}{2^{10}.3^9-2^{10}.3^{8}}\)
\(=\frac{2^{10}.3^8(1+5)}{2^{10}.3^8(3-1)}=\frac{6}{2}=3\)