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 #

\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^6\left(3^{25}+2^{30}\right)}{2^{11}.3^6\left(3^{25}+2^{30}\right)}=\frac{1}{2}\)

\(\frac{2^{10}.2^{31}+2^{40}.3^6}{2^{11}.2^{31}+2^{41}.3^6}\)

\(=\frac{2^{41}+2^{40}.3^6}{2^{42}+2^{41}.3^6}\)

\(=\frac{2^{40}\left(2+3^6\right)}{2^{41}\left(2+3^6\right)}\)

\(=\frac{1}{2}\)

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

\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)

\(=\frac{3^{17}\cdot\left(3^4\right)^{11}}{\left(3^3\right)^{10}\cdot\left(3^2\right)^{15}}\)

\(=\frac{3^{17}\cdot3^{44}}{3^{30}\cdot3^{30}}\)

\(=\frac{3^{61}}{3^{60}}\)

\(=3\)

\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)

\(=\frac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot\left(2\cdot3\right)^3}\)

\(=\frac{3^4\cdot2^{11}}{2^8\cdot2^3\cdot3^3}\)

\(=\frac{3^4\cdot2^{11}}{2^{11}\cdot3^3}\)

\(=\frac{3^4}{3^3}\)

\(=3\)

\(\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)

\(=\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2\cdot\left(2^{10}\cdot3^{31}+2^{40}\cdot3^6\right)}\)

\(=\frac{1}{2}\)

\(\frac{2^{10}.3^{31}+2^{90}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\) \(\frac{2^{10}.3^6.\left(3^{25}+2^{30}\right)}{2^{10}.3^6\left(3^{25}+2^{30}\right)}\) \(=1\)

\(=\frac{2^{10}\left(3^{31}+2^{30}.3^6\right)}{2^{11}\left(3^{31}+2^{30}.3^6\right)}=\frac{1}{2}\)