a) (\frac{1}{4})^5:\frac{1}{2^8}=[(\frac{1}{2})^2]^5:(\frac{1}{2})^8=(\frac{1}{2})^{10}:(\frac{1}{2})^8=(\frac{1}{2})^{10-8}=(\frac{1}{2})^2=\frac{1}{4}
b)
\frac{(-6)^4*(-2)^4}{12^2}=\frac{[(-6)*(-2)]^4}{12^2}=\frac{12^4}{12^2}=12^4-2)=12^2=144
c)
2^9:(-6^7:3^7)=2^9:(-6:3)^7=\frac{2^9}{(-2)^7}=-\frac{2^9}{2^7}=-2^{9-7}=-2^2=-4
d)
\frac{32^3}{8^2}=\frac{(2^5)^3}{(2^3)^2}=\frac{2^{15}}{2^6}=2^{15-6}=2^9=512
e)
\frac{81^4}{27^5}=\frac{(3^4)^4}{(3^3)^5}=\frac{3^{16}}{3^{15}}=3^{16-15}=3^1=3
f)
\frac{25^2*4^7}{2^9*5^4}=\frac{(5^2)^2*(2^2)^7}{5^*2^9}=\frac{5^4}{5^4}*\frac{2^{14}}{2^9}=1*2^{14-9}=2^5=32
g)
\frac{2^{10}*3^{10}}{6^8}=\frac{(2*3)^{10}}{6^8}=\frac{6^{10}}{6^8}=6^{10-8}=6^2=36
h)
\frac{5^8*2^9}{10^7}=\frac{5^8*2^8*2^1}{10^7}=\frac{(5*2)^8*2}{10^7}=\frac{10^8}{10^7}*2=10^{8-7}*2=10*2=20