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

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

cho mk cách đã bn 

\(\frac{512^4.128^6.64^2.2^{13}.4^7}{1024^2.64^5.128^3.8^4.512^4}=\frac{2^{117}}{2^{119}}=\frac{2^{117}}{2^{117}.2^2}=\frac{1}{2^2}=\frac{1}{4}\)

\(\frac{6^5+6^6.7}{6^3+6^6.4}=\frac{6^5.\left(1+6.7\right)}{6^3.\left(1+6^3.4\right)}\)

\(=\frac{6^2.43}{865}=\frac{36.43}{865}\)

\(=\frac{1568}{865}\)

k bn nha

\(\frac{9}{6}.\frac{6}{7}+\frac{9}{6}.\frac{4}{5}\)

\(=\frac{9}{6}\left(\frac{6}{7}+\frac{4}{5}\right)\)

\(=\frac{9}{6}\left(\frac{30}{35}+\frac{28}{35}\right)\)

\(=\frac{3}{2}.\frac{58}{35}\)

\(=\frac{174}{70}\)

\(=\frac{87}{35}\)