c) \( \left(\frac{m^{2} n^{8}}{m^{2} n^{10}}\right)\left(\frac{m^{5}}{m^{6}}\right)^{3} \)

To simplify the expression \( \left(\frac{m^{2} n^{8}}{m^{2} n^{10}}\right)\left(\frac{m^{5}}{m^{6}}\right)^{3} \), let's break it down step by step. Starting with the first part: \[ \frac{m^{2} n^{8}}{m^{2} n^{10}} \] Here, the \( m^{2} \) terms cancel out, resulting in: \[ \frac{n^{8}}{n^{10}} = n^{8-10} = n^{-2} \] Next, we consider the second part: \[ \left(\frac{m^{5}}{m^{6}}\right)^{3} \] This simplifies to: \[ \frac{m^{5}}{m^{6}} = m^{5-6} = m^{-1} \] Now we raise this to the power of 3: \[ (m^{-1})^{3} = m^{-3} \] Now, we can combine both results: \[ n^{-2} \cdot m^{-3} = \frac{1}{m^{3} n^{2}} \] Thus, the simplified expression is: \[ \frac{1}{m^{3} n^{2}} \]