donner la forme la plus simple de l'expression suivante [9×(3/4)^2×(-3/4)^4]÷(9/16)^2

[tex]\frac{9\times(\frac{3}{4})^{2}\times(\frac{-3}{4})^{4}}{(\frac{9}{16})^{2}} \\ \\ =\frac{9\times(\frac{3}{4})^{2}\times(\frac{3}{4})^{4}}{(\frac{3^{2}{4^{2})^{2}} \\ \\ =9\times\frac{(\frac{3}{4})^{2+4}}{(\frac{3}{4}^{2})^{2}} \\ \\ =9\times\frac{(\frac{3}{4})^{2+4}}{(\frac{3}{4})^{2\times2}} \\ \\ = 9\times(\frac{3}{4})^{6-4} \\ \\ = 9\times(\frac{3}{4})^{2} \\ \\ =\frac{9\times9}{16} \\ \\\\\boxed{=\frac{81}{16}}[/tex]


Règles :

[tex]a^{2}\times a^{3}=a^{2+3} \\ \\ \frac{a^{2}}{b^{2}}=(\frac{a}{b})^{2} \\ \\ (a^{2})^{3}=a^{2\times3} \\ \\ \frac{a^{3}}{a^{2}}=a^{3-2}[/tex]