a: \(A=\dfrac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=\dfrac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{11}\cdot3^{10}\cdot5}\)
\(=\dfrac{2}{3}\cdot\dfrac{6}{5}=\dfrac{12}{15}=\dfrac{4}{5}\)
b:
\(1-\dfrac{2}{a\left(a+1\right)}=\dfrac{a\left(a+1\right)-2}{a\left(a+1\right)}=\dfrac{a^2+a-2}{a\left(a+1\right)}=\dfrac{\left(a+2\right)\left(a-1\right)}{a\left(a+1\right)}\)
\(B=\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)\cdot...\cdot\left(1-\dfrac{1}{210}\right)\)
\(=\left(1-\dfrac{2}{6}\right)\left(1-\dfrac{2}{12}\right)\left(1-\dfrac{2}{20}\right)\cdot...\cdot\left(1-\dfrac{2}{420}\right)\)
\(=\left(1-\dfrac{2}{2\cdot3}\right)\left(1-\dfrac{2}{3\cdot4}\right)\left(1-\dfrac{2}{4\cdot5}\right)\cdot...\cdot\left(1-\dfrac{2}{20\cdot21}\right)\)
\(=\dfrac{\left(2+2\right)\left(2-1\right)}{2\left(2+1\right)}\cdot\dfrac{\left(3+2\right)\left(3-1\right)}{3\cdot\left(3+1\right)}\cdot...\cdot\dfrac{\left(20+2\right)\left(20-1\right)}{20\cdot\left(20+1\right)}\)
\(=\dfrac{4\cdot1}{2\cdot3}\cdot\dfrac{5\cdot2}{3\cdot4}\cdot...\cdot\dfrac{22\cdot19}{20\cdot21}\)
\(=\dfrac{4\cdot5\cdot...\cdot22}{2\cdot3\cdot...\cdot20}\cdot\dfrac{1\cdot2\cdot...\cdot19}{3\cdot4\cdot...\cdot21}\)
\(=\dfrac{4\cdot5\cdot21\cdot20}{1}\cdot\dfrac{1\cdot2}{20\cdot21}=\dfrac{4\cdot5\cdot1\cdot2}{1}=4\cdot5\cdot2=40\)
Giúp mình với aa (Giải chi tiết + nếu được thì thêm lời giải thích ở cuối bài làm giúp mình nha 
)
Giusp mình làm đề này nha!
