Simplify the expression. Write the answer with positive exponents only. Assume all variables represent nonzero real numbers. \[ \left(\frac{9 m^{-6} n^{2}}{3 m^{9} n^{-5}}\right)^{-1}= \]

First, let's simplify the inside of the expression \(\frac{9 m^{-6} n^{2}}{3 m^{9} n^{-5}}\). Dividing the coefficients, we have \( \frac{9}{3} = 3\). For the variables, we subtract the exponents: \( m^{-6 - 9} = m^{-15}\) and \( n^{2 - (-5)} = n^{2 + 5} = n^{7}\). So, we can rewrite the expression as \( 3 m^{-15} n^{7}\). Now we apply the negative exponent and take the reciprocal: \[ \left(3 m^{-15} n^{7}\right)^{-1} = \frac{1}{3 m^{-15} n^{7}} = \frac{n^{7}}{3 m^{-15}} = \frac{n^{7} m^{15}}{3} \] Therefore, the final simplified expression with positive exponents is: \[ \frac{n^{7} m^{15}}{3} \]