a)
\frac{4^{-6}*4^5}{4^{-2}}=\frac{4^{-1}}{4^{-2}}=4^{-1-(-2)}=4
b)
(\frac{1}{3})^{-4}*\frac{3^{-3}}{3^2}=3^4*3^{-3-2}=3^{4+(-5)}=3^{-1}=\frac{1}{3}
c)
(\frac{3}{2})^{-6}*(\frac{3}{2})^{2}*\frac{9^4}{8^3}=\frac{3^{-6}*3^2*3^8}{2^{-6}*2^2*2^9}=\frac{3^{-6+2+8}}{2^{-6+2+9}}=\frac{3^4}{2^5}=\frac{81}{32}=2\frac{17}{32}
d)
10^4*(\frac{4}{5})^{-3}*(5^5)^{-1}=2^4*5^4*\frac{5^3}{4^3}*\frac{1}{5^5}=16*\frac{5^7}{64*5^5}=\frac{1}{4}*5^{7-5}=\frac{5^2}{4}=\frac{25}{4}=6\frac{1}{4}
e)
2^{-5}*(\frac{1}{\sqrt2})^{-4}*\sqrt8^6=2^{-5}*(\sqrt2)^4*\sqrt{(2^3)^6}=2^{-5}*2^2*\sqrt{(2^9)^2}=2^{-3}*2^9=2^6=64