a)
3^4*(81*9^{-6})^{-1}=3^4*[3^4*(3^2)^{-6}]^{-1}=3^4*(3^{4+(-12)})^{-1}=3^4*(3^{-8})^{-1}=3^4*3^8=3^{12}
b)
125^3*0,2^{-7}=(5^3)^3*(\frac{1}{5})^{-7}=5^9*5^{-7}=5^2
c)
0,01*16*5^4=0,16*5^4=0,4^2*5^4=0,4^2*(5^2)^2=0,4^2*25^2=(0,4*25)^2=10^2
d)
2^4*9^2*36^{-5}=2^4*(3^2)^2*(6^2)^{-5}=2^4*3^4*6^{-10}=(2*3)^4*6^{-10}=6^{4+(-10)}=6^{-6}
e)
32^{-2}:(64^3*(\frac{1}{2})^{-3})=(2^5)^{-2}:[(2^6)^3*2^3]=2^{-10}:2^{18+3}=2^{-10}:2^{21}=2^{-31}
f)
(\frac{2}{3})^{-3}*(\frac{27}{8})^{-3}*1,5=(\frac{2}{3})^{-3}*((\frac{3}{2})^3)^{-3}*\frac{15}{10}=(\frac{3}{2})^3*(\frac{3}{2})^{-9}*\frac{3}{2}=
(\frac{3}{2})^{3-9+1}=(\frac{3}{2})^{-5}=(\frac{2}{3})^5