[tex][(\frac{-3}{2})^{2}]^{6}=(\frac{3^{2}}{2^{2}})^{6}=\frac{3^{12}}{2^{12}} [/tex]
[tex][(\frac{5}{3})^{-2}] ^{3}=[(\frac{3}{5})^{2}]^{3}=(\frac{3}{5})^{6}=\frac{3^{6}}{5^{6}} [/tex]
[tex][(\frac{2}{5})^{2}]^{-3}=(\frac{2^{2}}{5^{2}})^{-3}=(\frac{5^{2}}{2^{2}})^{3}=\frac{5^{6}}{2^{6}} [/tex]
[tex]16^{-1}=(2^{4})^{-1}=2^{-4} [/tex]
[tex](\frac{-4}{9})^{6}=(\frac{2^{2}}{3^{2}})^{6}=\frac{2^{12}}{3^{12}} [/tex]
On a donc :
[tex]B=\frac{\frac{3^{12}}{2^{12}}*\frac{3^{6}}{5^{6}}*\frac{5^{6}}{2^{6}}}{2^{-4}*\frac{3^{12}}{2^{12}}*3^{4}} [/tex]
[tex]B= \frac{\frac{3^{6}}{2^{6}}}{\frac{3^{4}}{2^{4}}} [/tex]
[tex]B=\frac{(\frac{3}{2})^{6}}{(\frac{3}{2})^{4}}=(\frac{3}{2})^{6-4} [/tex]
[tex]B=(\frac{3}{2})^{2}=\frac{9}{4}=2,25 [/tex]
