\(\dfrac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.\left(2^2.5\right)}\)

\(=\dfrac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}=\dfrac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)

\(=\dfrac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}=\dfrac{-2}{6}=-\dfrac{1}{3}\)

\(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\\ =\dfrac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^8\cdot3^8\cdot2^2\cdot5}\\ =\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\\ =\dfrac{2^{10}\cdot3^8\cdot\left(1-3\right)}{2^{10}\cdot3^8\cdot\left(1+5\right)}\\ =\dfrac{-2}{6}\\ =-\dfrac{1}{3}\)

\(M=\left(100-1\right)\left(100-2^2\right)\left(100-3^2\right).....\left(100-50^2\right)\\ =\left(100-1\right)\left(100-2^2\right)\left(100-3^2\right).....\left(100-10^2\right).....\left(100-50^2\right)\\ =\left(100-1\right)\left(100-2^2\right)\left(100-3^2\right).....\left(100-100\right).....\left(100-50^2\right)\\ =\left(100-1\right)\left(100-2^2\right)\left(100-3^2\right)....0....\left(100-50^2\right)=0\)

dạng toán này được gọi là gì v ạ?

a: Xét ΔABD vuông tại A và ΔEBD vuông tại E có

BD chung

\(\widehat{ABD}=\widehat{EBD}\)

Do đó: ΔBAD=ΔBED

=>DA=DE

b: DA=DE

=>D nằm trên đường trung trực của AE(1)

Ta có: BA=BE

=>B nằm trên đường trung trực của AE(2)

Từ (1),(2) suy ra BD là đường trung trực của AE

mà BD cắt AE tại F

nên F là trung điểm của AE

=>CF là đường trung tuyến của ΔAEC

nhanh giúp với ạ

\(\dfrac{x-85}{15}+\dfrac{x-74}{13}+\dfrac{x-67}{11}+.\dfrac{x-64}{9}=10\\ \Leftrightarrow\left(\dfrac{x-85}{15}-1\right)+\left(\dfrac{x-74}{13}-2\right)+\left(\dfrac{x-67}{11}-3\right)+\left(\dfrac{x-64}{9}-4\right)=0\\ \Leftrightarrow\dfrac{x-100}{15}+\dfrac{x-100}{13}+\dfrac{x-100}{11}+\dfrac{x-100}{9}=0\\ \Leftrightarrow\left(x-100\right)\left(\dfrac{1}{15}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}\right)=0\\ \Leftrightarrow x-100=0\\ \Leftrightarrow x=100\)

\(\dfrac{x-85}{15}+\dfrac{x-74}{13}+\dfrac{x-67}{11}+\dfrac{x-64}{9}=10\\\dfrac{x-85}{15}+\dfrac{x-74}{13}+\dfrac{x-67}{11}+\dfrac{x-64}{9}-10=0\\ \left(\dfrac{x-85}{15}-1\right)+\left(\dfrac{x-74}{13}-2\right)+\left(\dfrac{x-67}{11}-3\right)+\left(\dfrac{x-64}{9}-4\right)=0 \\ \dfrac{x-85-15}{15}+\dfrac{x-74-26}{13}+\dfrac{x-67-33}{11}+\dfrac{x-64-36}{9}=0\\ \dfrac{x-100}{15}+\dfrac{x-100}{13}+\dfrac{x-100}{11}+\dfrac{x-100}{9}=0\\ \left(x-100\right)\cdot\left(\dfrac{1}{15}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}\right)=0\)

Vì \(\dfrac{1}{15}+\dfrac{1}{13}+\dfrac{1}{11}+\dfrac{1}{9}\ne0\)

\(A=3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\\ 3A=3^{101}-3^{100}+3^{99}-3^{98}+...+3^3-3^2+3\\ 3A+A=\left(3^{101}-3^{100}+3^{99}-3^{98}+...+3^3-3^2+3\right)+\left(3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\right)\\ 4A=3^{101}+\left(3^{100}-3^{100}\right)+\left(3^{99}-3^{99}\right)+...+\left(3^2-3^2\right)+\left(3-3\right)-1\\ 4A=3^{101}-1\\ A=\dfrac{3^{101}-1}{4}\)

Nếu đề bài là: (\(\dfrac{2}{3}\))⁵ x \(\dfrac{1}{2^5}\) thì làm như này em nhé.

(\(\dfrac{2}{3}\))⁵ x \(\dfrac{1}{2^5}\) = (\(\dfrac{2}{3}\) x \(\dfrac{1}{2}\))⁵ = (\(\dfrac{1}{3}\))⁵  

\(\dfrac{11}{8}\left[\left(\dfrac{-5}{11}:\dfrac{13}{8}-\dfrac{5}{11}:\dfrac{13}{5}\right)+\dfrac{-6}{33}\right]+\dfrac{3}{4}\\ =\dfrac{11}{8}\left[\left(\dfrac{-5}{11}\cdot\dfrac{8}{13}+\dfrac{-5}{11}\cdot\dfrac{5}{13}\right)+\dfrac{-2}{11}\right]+\dfrac{3}{4}\\ =\dfrac{11}{8}\left[\dfrac{-5}{11}\cdot\left(\dfrac{8}{13}+\dfrac{5}{13}\right)+\dfrac{-2}{11}\right]+\dfrac{3}{4}\\ =\dfrac{11}{8}\left(\dfrac{-5}{11}+\dfrac{-2}{11}\right)+\dfrac{3}{4}\\ =\dfrac{11}{8}\cdot\dfrac{-7}{11}+\dfrac{3}{4}\\ =\dfrac{-7}{8}+\dfrac{6}{8}\\ =\dfrac{-1}{8}\)