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\(a,\frac{5\cdot6+5\cdot7}{5\cdot8+20}=\frac{\left(5\cdot6+5\cdot7\right)\div2}{\left(5.8+20\right)\div2}=\frac{13}{12}\)
\(\frac{8.9-4.15}{12.7-180}=\frac{12.6-12.5}{12.7-12.15}=\frac{1}{-8}=\frac{-1}{8}\)
\(Ta\)\(co\)\(\frac{13}{12}=\frac{13.2}{12.2}=\frac{26}{24}\)
\(\frac{-1}{8}=\frac{3\left(-1\right)}{3.8}=\frac{-3}{24}\)
Phần b bạn tính ra rồi làm tương tự phần a nha chúc bạn học giỏi!!!
Giải:
\(10.\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=10.\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10.\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=10.\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=10.\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}\)
\(=10.\dfrac{2^{13}.3^{11}}{2^{11}.3^{11}.5}\)
\(=10.\dfrac{2^2}{5}\)
\(=2^3=8\)
Vậy ...
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: \(B=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)
\(a,\dfrac{-5}{8};\dfrac{7}{10};\dfrac{16}{19};\dfrac{20}{23}\)
\(\Rightarrow\dfrac{20}{23}>\dfrac{16}{19}>\dfrac{7}{10}>\dfrac{-5}{8}\)
Vậy \(\dfrac{20}{23}>\dfrac{16}{19}>\dfrac{7}{10}>\dfrac{-5}{8}\)
\(b,\dfrac{5\times6+6\times7}{5\times5+20}\)và \(\dfrac{8\times9-4\times15}{12\times7-180}\)
Xét : \(\dfrac{5\times6+6\times7}{5\times5+20}\)
\(=\dfrac{\left(5+7\right)\times6}{5\times5+5\times4}\)
\(=\dfrac{12\times6}{\left(5+4\right)\times5}\)
\(=\dfrac{72}{9\times5}\)
\(=\dfrac{72}{45}\)
\(=\dfrac{8}{5}\)
Xét : \(\dfrac{8\times9-4\times15}{12\times7-180}\)
\(=\dfrac{72-60}{84-180}\)
\(=\dfrac{12}{-96}\)
\(=\dfrac{-1}{8}\)
Quy đồng \(\dfrac{8}{5}=\dfrac{8\times8}{5\times8}=\dfrac{64}{40}\\ \dfrac{-1}{8}=\dfrac{\left(-1\right)\times5}{8\times5}=\dfrac{-5}{40}\)
Vì \(\dfrac{64}{40}>\dfrac{-5}{40}\)
\(\Rightarrow\dfrac{8}{5}>\dfrac{-1}{8}\)
\(\Rightarrow\dfrac{5\times6+6\times7}{5\times5+20}>\dfrac{8\times9-4\times15}{12\times7-180}\)
Vậy \(\dfrac{5\times6+6\times7}{5\times5+20}>\dfrac{8\times9-4\times15}{12\times7-180}\)
a) \(\dfrac{2727-101}{3.303+404}=\dfrac{2626}{909+404}=\dfrac{2626}{1313}=2\)
b) \(\dfrac{8.9-4.15}{12.7-180}=\dfrac{72-60}{84-180}=\dfrac{12}{-96}=\dfrac{-1}{8}\)
c) \(\dfrac{-19}{3^2.7.11}=\dfrac{-19}{9.7.11}=\dfrac{-19}{63.11}=\dfrac{-19}{693}\)
d) \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+120.6^9}{2^{12}.3^{12}-6^{11}}=\dfrac{2^2.6^{10}+20.6.6^9}{6^{12}-6^{11}}=\dfrac{4.6^{10}+20.6^{10}}{6^{11}\left(6-1\right)}=\dfrac{\left(4+20\right).6^{10}}{5.6^{11}}=\dfrac{24}{30}=\dfrac{4}{5}\)
có cách nào khác nữa ko bạn