\(\left(\frac{3}{5}\right)^{2012}:\left(\frac{9}{25}\right)^{1000}=\left(\frac{3}{5}\right)^{2012}:\left(\frac{3}{5}\right)^{2000}=\left(\frac{3}{5}\right)^{12}\)
\(\left(\frac{3}{5}\right)^{2012}:\left(\frac{9}{25}\right)^{1000}=\left(\frac{3}{5}\right)^{2012}:\left[\left(\frac{3}{5}\right)^2\right]^{1000}=\left(\frac{3}{5}\right)^{2012}:\left(\frac{3}{5}\right)^{2000}\)
\(=\left(\frac{3}{5}\right)^{12}\)