\(=\frac{3^7\cdot\left(2^4\right)^3}{\left(2^2\cdot3\right)^5\cdot\left(3^3\right)^2}\)    

\(=\frac{3^7\cdot2^{12}}{2^{10}\cdot3^5\cdot3^6}\)    

\(=\frac{3^7\cdot2^{12}}{2^{10}\cdot3^{11}}\)   

\(=\frac{2^2}{3^4}\)   

\(=\frac{4}{81}\)

\(\frac{3^7.16^3}{12^5.27^2}=\frac{3^7.\left(2^4\right)^3}{\left(2^2.3\right)^5.\left(3^3\right)^2}=\frac{3^7.2^{12}}{2^{10}.3^5.3^6}=\frac{3^7.2^{12}}{2^{10}.3^{11}}=\frac{2^2}{3^4}=\frac{4}{81}\)

\(\frac{3^7.16^3}{12^5.27^2}=\frac{3^7.\left(2^4\right)^3}{\left(2^2.3\right)^5.\left(3^3\right)^2}=\frac{3^7.2^{12}}{2^{10}.3^{11}}=\frac{2^2}{3^4}\)

\(\frac{2^7.6^{15}}{16^5.27^6}=\frac{2^7.\left(2.3\right)^{15}}{\left(2^4\right)^5.\left(3^3\right)^6}=\frac{2^7.2^{15}.3^{15}}{2^{20}.3^{18}}=\frac{2^{22}.3^{15}}{2^{20}.3^{18}}=\frac{2^2.1}{1.3^3}=\frac{4}{27}\)

\(\frac{9^5.27^3}{3^{18}}=\frac{\left(3^2\right)^5.\left(3^3\right)^3}{3^{18}}=\frac{3^{10}.3^9}{3^{18}}=\frac{3^{19}}{3^{18}}=3^{19-18}=3^1=3\)

k mk nha !

\(\frac{9^5.27^3}{3^{18}}=\frac{\left(3^2\right)^5.\left(3^3\right)^3}{3^{18}}=\frac{3^{10}.3^9}{3^{18}}=3^{19-18}=3^1=3.\)

P/S : Good Luck
~Best Best~

A= 648

a) \(\frac{9^{10}.27^7}{81^7.3^{15}}\)= \(\frac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}\)= \(\frac{3^{2.10}.3^{3.7}}{3^{4.7}.3^{15}}\)=\(\frac{3^{20}.3^{21}}{3^{28}.3^{15}}\)=\(\frac{3^{41}}{3^{43}}\)= \(\frac{3^{41}}{3^{41}.3^2}\)= \(\frac{1}{3^2}=\frac{1}{9}\)

b) \(\frac{8^3.9^5.27^5}{4^5.81^6}\)= \(\frac{\left(2^3\right)^3.\left(3^2\right)^5.\left(3^3\right)^5}{\left(2^2\right)^5.\left(3^4\right)^6}\)= \(\frac{2^{3.3}.3^{2.5}.3^{3.5}}{2^{2.5}.3^{4.6}}\)=\(\frac{2^9.3^{10}.3^{15}}{2^{10}.3^{24}}\)= \(\frac{2^9.3^{25}}{2^{10}.3^{24}}\)=\(\frac{2^9.3^{24}.3}{2^9.2.3^{24}}\)=\(\frac{3}{2}\)

a) $\frac{4}{{25}}:\frac{4}{3} = \frac{4}{{25}} \times \frac{3}{4} = \frac{3}{{25}}$ 

b) $\frac{3}{{14}}:\frac{6}{7} = \frac{3}{{14}} \times \frac{7}{6} = \frac{{3 \times 7}}{{14 \times 6}} = \frac{{3 \times 7}}{{7 \times 2 \times 3 \times 2}} = \frac{1}{4}$

c) $\frac{{12}}{{15}}:2 = \frac{{12}}{{15}} \times \frac{1}{2} = \frac{{12 \times 1}}{{15 \times 2}} = \frac{{6 \times 2 \times 1}}{{15 \times 2}} = \frac{6}{{15}}$           

d) $\frac{{21}}{8}:6 = \frac{{21}}{8} \times \frac{1}{6} = \frac{{21 \times 1}}{{8 \times 6}} = \frac{{7 \times 3 \times 1}}{{8 \times 3 \times 2}} = \frac{7}{{16}}$