1) \(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}=\frac{3^{2014}.\left(2^3\right)^{19}}{\left(2.3\right)^{60}.3^{1955}}=\frac{3^{2014}.2^{57}}{2^{60}.3^{2015}}=\frac{1}{2^3.3}=\frac{1}{24}\)
2) \(5^x+5^{x+1}=150\)
=> 5x(1 + 5) = 150
=> 5x.6 = 150
=> 5x = 25
=> \(x=\pm2\)
3) \(\frac{3}{11.16}+\frac{3}{16.21}+...+\frac{3}{61.66}=\frac{3}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)
\(=\frac{3}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)=\frac{3}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{3}{5}.\frac{5}{66}=\frac{1}{22}\)
cảm ơn bạn Xyz đã trả lời
Bài 1:
\(\frac{3^{2014}.8^{19}}{6^{60}.3^{1955}}=\frac{3^{59}.2^{57}}{2^{60}.3^{60}}=\frac{1}{24}\)
Bài 2:
\(5^x+5^{x+1}=150\\ 5^x+5^x.5=150\\ 5^x\left(1+5\right)=150\\ 5^x.6=150\\ 5^x=25=>x=2\)
Bài 3:
A = \(3\left(\frac{1}{11.16}+\frac{1}{16.21}+\frac{1}{21.26}+...+\frac{1}{61.66}\right)=\frac{5}{3}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)=\frac{5}{3}.\frac{5}{66}=\frac{25}{198}\)
