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

b)  \(\frac{4}{10}+\frac{-2}{9}+\frac{-3}{-5}+\frac{21}{-27}+\frac{-10}{20}\)

\(=\frac{2}{5}-\frac{2}{9}+\frac{3}{5}-\frac{7}{9}-\frac{1}{2}\)

\(=\left(\frac{2}{5}+\frac{3}{5}\right)-\left(\frac{2}{9}+\frac{7}{9}\right)-\frac{1}{2}\)

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

a)  \(-\frac{5}{2}+\frac{1}{7}+\frac{6}{7}+\frac{1}{2}+\frac{3}{4}\)

\(=\left(\frac{-5}{2}+\frac{1}{2}\right)+\left(\frac{1}{7}+\frac{6}{7}\right)+\frac{3}{4}\)

\(=-2+1+\frac{3}{4}\)

\(=-1+\frac{3}{4}\)

\(=-\frac{1}{4}\)

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

\(\frac{18}{27}-\frac26\)

\(=\frac23-\frac13=\frac{2-1}{3}=\frac13\)

\(\frac{37}{12}-3=\frac{37}{12}-\frac{36}{12}=\frac{37-36}{12}=\frac{1}{12}\)

\(5-\frac{14}{3}=\frac{15}{3}-\frac{14}{3}=\frac{15-14}{3}=\frac13\)

\(\frac{10}{21}:\frac23=\frac{10}{21}\times\frac32=\frac{30}{42}=\frac57\)

\(\frac35:\frac34=\frac35\times\frac43=\frac33\times\frac45=\frac45\)

\(\frac25:\frac{3}{10}=\frac25\times\frac{10}{3}=\frac{20}{15}=\frac43\)

\(\frac38:\frac94=\frac38\times\frac49=\frac{12}{72}=\frac16\)

\(\frac{8}{21}:\frac47=\frac{8}{21}\times\frac74=\frac{7}{21}\times\frac84=\frac23\)

\(\frac85:\frac{15}{8}=\frac85\times\frac{8}{15}=\frac{64}{75}\)

Bài 1:

A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + (\(\frac45\) - \(\frac{3}{17}\) + \(\frac13\)) - \(\frac17\) + (- \(\frac{14}{30}\))

A = \(\frac15\) + \(\frac{3}{17}\) - \(\frac43\) + \(\frac45\) - \(\frac{3}{17}\) + \(\frac13\) - \(\frac17\) - \(\frac{14}{30}\)

A = (\(\frac15\) + \(\frac45\)) + (\(\frac{3}{17}\) - \(\frac{3}{17}\)) - (\(\frac43-\frac13\)) - \(\frac{30}{210}\) - \(\frac{98}{210}\)

A = 1 + 0 - 1 - (\(\frac{30}{210}+\frac{98}{210}\))

A = 1 - 1 - \(\frac{228}{210}\)

A = 0 - \(\frac{128}{210}\)

A = - \(\frac{64}{105}\)

Bài 2:

B= (\(\frac58\) - \(\frac{4}{12}\) + \(\frac32\)) - (\(\frac58\) + \(\frac{9}{13}\)) - (\(\frac{-3}{2}\)) + \(\frac{7}{-15}\)

B = \(\frac58\) - \(\frac{4}{12}\) + \(\frac32\) - \(\frac58\) - \(\frac{9}{13}\) + \(\frac32\) - \(\frac{7}{15}\)

B = (\(\frac58\) - \(\frac58\)) + (\(\frac32\) + \(\frac32\)) - (\(\frac13\) + \(\frac{9}{13}\) + \(\frac{7}{15}\))

B = 0 + 3 - (\(\frac{65}{195}\) + \(\frac{135}{195}\) + \(\frac{91}{195}\))

B = 3 - (\(\frac{200}{195}\) + \(\frac{91}{195}\))

B = 3 - \(\frac{97}{65}\)

B = \(\frac{195}{65}\) - \(\frac{97}{65}\)

B = \(\frac{98}{65}\)

ai nhanh nhất mà trả lời dúng mik tặng 3 k

a: Ta có: \(\left(-\frac57-\frac79+\frac{9}{11}-\frac{11}{13}\right)\cdot\left(3-\frac34\right)\)

\(=\left(-\frac{6435}{9009}-\frac{7007}{9009}+\frac{7371}{9009}-\frac{7623}{9009}\right)\cdot\frac94\)

\(=-\frac{13694}{9009}\cdot\frac94=\frac{-6847}{2}\cdot\frac{1}{1001}=\frac{-6847}{2002}\)

b: \(\left(\frac{10}{21}+\frac{14}{27}-\frac{6}{11}+\frac{22}{39}\right):\left(2-\frac23\right)\)

\(=\left(\frac{12870}{27027}+\frac{14014}{27027}-\frac{14742}{27027}+\frac{15246}{27027}\right):\frac43\)

\(=\frac{27388}{27027}\cdot\frac34=\frac{6847}{9009}\)