\(25^{10}.\left(\frac{1}{5}\right)^{20}+\left(\frac{3}{4}\right)^8.\left(\frac{-4}{3}\right)^8-2011^0\)
\(=5.5^{10}.\left(\left(\frac{1}{5}\right)^2\right)^{10}+\left(\frac{3}{4}\right)^8.\left(\frac{-4}{3}\right)^8-1\)
\(=\left(5.\left(\frac{1}{5}\right)^2\right)\left(\frac{5}{5}\right)^{10}+\left(-1\right)^8-1\)
\(=\frac{1}{5}.1+1-1\)
\(=\frac{1}{5}\)