a)
12^3*12^{-2}*12^{-6}=12^{3+(-2)+(-6)}=12^{3-2-6}=12^{-5}
b)
7^{-4}:7^5:7^{-6}=7^{-4-5-(-6)}=7^{-4-5+6}=7^{-3}
c)
(\frac{2}{5})^{-5}:(\frac{2}{5})^{-2}*(\frac{2}{5})^6=(\frac{2}{5})^{-5+2+6}=(\frac{2}{5})^3
d)
(\frac{7}{9})^{-3}*(\frac{7}{9})^{-1}:(\frac{7}{9})^{-2}=(\frac{7}{9})^{-3-1+2}=(\frac{7}{9})^{-2}
e)
265^{-36}:265^{-9}*265^{15}=265^{-36+9+15}=265^{-12}
f)
(\frac{2}{5})^{-5}:((\frac{2}{5})^{-2}*(\frac{2}{5})^6)=(\frac{2}{5})^{-5}:(\frac{2}{5})^{-2+6}=(\frac{2}{5})^{-5-4}=(\frac{2}{5})^{-9}