Simplify the expression. Write the answer with positive exponents only. Assume all variables represent nonzero real numbers. \[ \frac{m^{-6} n^{-6}}{m^{0} n^{9}}= \]

To simplify the expression \(\frac{m^{-6} n^{-6}}{m^{0} n^{9}}\), start by applying the properties of exponents. We know that \(m^{0} = 1\), so the expression becomes \(\frac{m^{-6} n^{-6}}{1 \cdot n^{9}}\) or simply \(\frac{m^{-6} n^{-6}}{n^{9}}\). Now, simplifying the \(n\) terms in the denominator and the numerator gives us: \[ m^{-6} n^{-6} \cdot n^{-9} = m^{-6} n^{-6 - 9} = m^{-6} n^{-15} \] Next, we convert negative exponents to positive exponents by using the property that \(a^{-b} = \frac{1}{a^b}\): \[ m^{-6} n^{-15} = \frac{1}{m^{6} n^{15}} \] Thus, the simplified expression with positive exponents is: \[ \frac{1}{m^{6} n^{15}} \]