To simplify the expression, we can break it down step by step:
\(0.001^{-1}\): \(0.001^{-1} = \frac{1}{0.001} = 1000\).
\(3-(-2)^{-2}\): Calculate \((-2)^{-2}\) first, which is \(\frac{1}{(-2)^2} = \frac{1}{4}\). So, \(3-(-2)^{-2} = 3 - \frac{1}{4} = \frac{12 - 1}{4} = \frac{11}{4}\).
\(64^{2/3}\): \(64^{2/3} = (64^{1/3})^2 = (4)^2 = 16\).
\(8^{-1/3}\): \(8^{-1/3} = \frac{1}{8^{1/3}} = \frac{1}{2}\).
\(1 + 9^0\): \(9^0\) is equal to 1, so \(1 + 1 = 2\).
Now combining all the results we got:
\(1000 + \frac{11}{4} + 16 + \frac{1}{2} + 2\)
\(= 1000 + \frac{11}{4} + 16 + \frac{1}{2} + 2\)
\(= 1000 + 2.75 + 16 + 0.5 + 2\)
\(= 1021.25 + 16 + 2\)
\(= 1039.25\).
Therefore, the simplified result of the expression is \(1039.25\).