\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{11}.3^6}\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2}{2+2}=\frac{2}{4}=\frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài làm
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{11}+2^{41}.3^6}\)
\(=\frac{2^{10}.\left(3^{11}+2^{30}.3^6\right)}{2^{11}.\left(3^{11}+2^{30}.3^6\right)}\)
\(=\frac{1}{2}\)
~ K chắc ~
# Học tốt #
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^6\left(3^{25}+2^{30}\right)}{2^{11}.3^6\left(3^{25}+2^{30}\right)}=\frac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)
\(=\frac{3^{17}\cdot\left(3^4\right)^{11}}{\left(3^3\right)^{10}\cdot\left(3^2\right)^{15}}\)
\(=\frac{3^{17}\cdot3^{44}}{3^{30}\cdot3^{30}}\)
\(=\frac{3^{61}}{3^{60}}\)
\(=3\)
\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)
\(=\frac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot\left(2\cdot3\right)^3}\)
\(=\frac{3^4\cdot2^{11}}{2^8\cdot2^3\cdot3^3}\)
\(=\frac{3^4\cdot2^{11}}{2^{11}\cdot3^3}\)
\(=\frac{3^4}{3^3}\)
\(=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{99\cdot101}\)
\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{99}-\frac{1}{101}\)
\(2A=\frac{100}{101}\)
\(A=\frac{50}{101}\)
b) \(\frac{2^{10}+3^{31}+2^{40}+3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}=\frac{2^{10}+2^{40}}{2^{11}+2^{41}}\)
\(\frac{2^{10}+2^{40}}{2^{11}+2^{41}}=\frac{1}{2}\)
=1/2x(1/1.3+1/3.5+...+1/99.101)
=1/2.(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=1/2.(1-1/101)
=1/2.100/101
=50/101
chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{2^{10}.3^{31}+2^{90}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\) \(\frac{2^{10}.3^6.\left(3^{25}+2^{30}\right)}{2^{10}.3^6\left(3^{25}+2^{30}\right)}\) \(=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\frac{2^{10}\left(3^{31}+2^{30}.3^6\right)}{2^{11}\left(3^{31}+2^{30}.3^6\right)}=\frac{1}{2}\)