a). Simplity Exporents 1.] \( \frac{-12 a^{19}}{-18 a^{6}} \)

To simplify the expression \( \frac{-12 a^{19}}{-18 a^{6}} \), start by canceling out the negative signs. This gives you \( \frac{12 a^{19}}{18 a^{6}} \). Next, simplify the coefficients: \( \frac{12}{18} = \frac{2}{3} \). Now focus on the variables; using the property \( \frac{a^m}{a^n} = a^{m-n} \), we get \( a^{19 - 6} = a^{13} \). So the final answer is \( \frac{2}{3} a^{13} \). To put it plainly, simplifying fractions with exponents is like finding the best way to organize your closet—you're just putting the bigger pieces in order and getting rid of the excess baggage!