lg2×lg2500+2lg5^2+9^2+log9^3

Using the properties of logarithms, we can simplify this expression as follows:

lg2×lg2500+2(lg5)^2+9^2+log9^3 = lg(2×2500) + 2(lg5)^2 + 81 + log(729) = lg(5000) + 2(25) + 81 + 3 = lg(5000) + 56 = lg(5×10^3) + 56 = lg5 + lg(10^3) + 56 = lg5 + 3 + 56 = lg5 + 59

Therefore, the simplified expression is lg5 + 59.