\(\frac{2^{11}\cdot9^2}{3^5\cdot16^2}\)

\(=\frac{2^{11}\cdot3^4}{3^5\cdot2^8}\)

\(=\frac{2^3}{3}\)

\(=\frac{8}{3}\)

\(\frac{2^{11}\cdot9^2}{3^5\cdot16^2}=\frac{2^{11}\cdot\left(3^2\right)^2}{3^5\cdot\left(2^4\right)^2}=\frac{2^{11}\cdot3^4}{3^5\cdot2^8}=\frac{2^3}{3}=\frac{8}{3}\)

a) \(k=\frac{2^{11}.9^2}{3^5.16^2}=\frac{2^{11}.\left(3^2\right)^2}{3^5.\left(2^4\right)^2}=\frac{2^{11}.3^4}{3^5.2^8}=\frac{8.1}{3.1}=\frac{8}{3}\)

b)  \(N=\frac{9^3.27^2}{6^2.3^{10}}=\frac{\left(3^2\right)^3.\left(3^3\right)^2}{\left(2.3\right)^2.3^{10}}=\frac{3^6.3^6}{2^2.3^2.3^{10}}=\frac{3^{12}}{4.3^{12}}=\frac{1}{4}\)

c)\(P=\frac{\left(3^3\right)^{25}.5^3.\left(2^3\right)^4}{\left(5^2\right)^2.\left(3^4\right)^{11}.2^{11}}=\frac{3^{75}.5^3.2^{12}}{5^4.3^{44}.2^{11}}=\frac{3^{31}.1.2}{5.1.1}=\frac{3^{31}.2}{5}=....\)

a) \(K=\frac{2^{11}\cdot9^2}{3^5\cdot16^2}=\frac{2^{11}\cdot3^4}{3^5\cdot2^8}=\frac{2^3}{3}=\frac{8}{3}\)

b) \(N=\frac{9^3\cdot27^2}{6^2\cdot3^{10}}=\frac{3^6\cdot3^6}{2^2\cdot3^2\cdot3^{10}}=\frac{1}{4}\)

c) \(P=\frac{27^{15}\cdot5^3\cdot8^4}{25^2\cdot81^{11}\cdot2^{11}}=\frac{3^{45}\cdot5^3\cdot2^{12}}{5^4\cdot3^{44}\cdot2^{11}}=\frac{3\cdot2}{5}=\frac{6}{5}\)

\(\dfrac{\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{9}+\dfrac{2}{13}}{\dfrac{11}{3}-\dfrac{11}{5}+\dfrac{11}{9}+\dfrac{11}{13}}\)

\(=\dfrac{2\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{9}+\dfrac{1}{13}\right)}{11\cdot\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{9}+\dfrac{1}{13}\right)}\)

\(=\dfrac{2}{11}\)

8: \(=\dfrac{-5}{9}-\dfrac{4}{9}+\dfrac{8}{15}+\dfrac{7}{15}-\dfrac{2}{11}=\dfrac{-2}{11}\)

9: =2/7-2/5+5/7=1-2/5=3/5

10: \(=\dfrac{7}{19}\left(\dfrac{8}{11}+\dfrac{3}{11}\right)-\dfrac{12}{19}=\dfrac{-5}{19}\)

11: \(=\dfrac{-5}{7}\left(\dfrac{2}{11}+\dfrac{9}{11}\right)=\dfrac{-5}{7}\)

8 = -2/11

9 = 3/5

10 = -5/19

11 = -5/7

11 = 5/13

\(A=\dfrac{-19}{9}.\dfrac{1}{2}-\dfrac{4}{11}.\dfrac{-11}{9}+\left(-\dfrac{2}{3}\right)=-\dfrac{23}{18}\)

\(B=\left(-\dfrac{15}{6}\right):\dfrac{-1}{2}+\dfrac{7}{-12}-\dfrac{1}{3}.\dfrac{-11}{2}=\dfrac{25}{4}\)

\(C=\dfrac{3}{4}.\left(-8\right)-\dfrac{1}{3}.\dfrac{-7}{2}-\dfrac{5}{18}=-\dfrac{46}{9}\)

\(A=\dfrac{-19}{18}+\dfrac{4}{9}-\dfrac{2}{3}=\dfrac{-19}{18}+\dfrac{8}{18}-\dfrac{12}{18}=\dfrac{-23}{18}\)

\(B=\dfrac{-5}{2}\cdot\dfrac{-2}{1}-\dfrac{7}{12}+\dfrac{11}{6}=\dfrac{5\cdot12-7+22}{12}=\dfrac{75}{12}=\dfrac{25}{4}\)

  chúc bạn học tốt

a. 2/11 + ( -14/11 ) 

= -12/11

b. 1/4 + ( -3/6 + 4/6 ) 

= 1/4 + 1/6 

= 6/24 + 4/24

= 10/24

= 5/12

a, \(\dfrac{2}{11}\) + [ \(-\dfrac{5}{11}\) - \(\dfrac{9}{11}\)]

= \(\dfrac{2}{11}\) + [ \(-\dfrac{14}{11}\)]

= \(\dfrac{2-14}{11}\)

= \(-\dfrac{12}{11}\)

b, \(\dfrac{1}{4}\) + ( \(-\dfrac{1}{2}\) + \(\dfrac{2}{3}\))

= \(\dfrac{1}{4}\) + ( \(-\dfrac{3}{6}\) + \(\dfrac{4}{6}\))

= \(\dfrac{1}{4}\) + \(\dfrac{1}{6}\)

= \(\dfrac{3}{12}\) + \(\dfrac{2}{12}\)

= \(\dfrac{5}{12}\)

a)338800/539000=22/35

b)60/20=1/3