12 Simplify. \( \frac{63 m^{5} n^{6}}{27 m n} \)

To simplify the expression \( \frac{63 m^{5} n^{6}}{27 m n} \), we can start by factoring out the common terms. First, simplify the coefficients: \( \frac{63}{27} = \frac{7}{3} \). Next, for the variable \( m \), \( \frac{m^5}{m} = m^{5-1} = m^{4} \) and for \( n \), \( \frac{n^6}{n} = n^{6-1} = n^{5} \). Putting it all together, the simplified expression is \( \frac{7 m^{4} n^{5}}{3} \). Enjoy this streamlined version of your algebraic adventure! And remember, with every mathematical journey, practice makes perfect! Keep solving different kinds of expressions to become more comfortable with simplification techniques, and soon enough, you’ll tackle even more complex equations with ease.