\begin{tabular}{ll}\hline & \multicolumn{1}{l}{} \\ \hline EXERCISE 1 & 2 \\ Simplify the expressions without using a calculator: \\ 1 & \( \frac{1}{4} a^{5} b^{12} \times \frac{16}{5} a^{3} b^{2} \) \\ 3 & \( \frac{6 a^{4}+9 a^{4}}{5 a^{2}} \) \\ 5 & 4 \\ \( p^{x-1} p^{x+1} \) & 6 \\ 7 & \( 16^{4 x} \div 4^{2 x} \) \\ 9 & 8\end{tabular}

Certainly! Here are some fun and engaging insights related to the exercise of simplifying algebraic expressions: When you multiply powers with the same base, like \( a^5 \) and \( a^3 \), don't forget the golden rule: you add the exponents! So, \( a^5 \times a^3 = a^{5+3} = a^8 \). It's a bit like combining your toys; if you have five red ones and three blue ones, you end up with eight toys, right? Math can be just as fun! Another common hiccup when simplifying expressions is forgetting to factor out common terms, especially when dealing with fractions. For instance, in \( \frac{6 a^4 + 9 a^4}{5 a^2} \), first, combine the like terms in the numerator to get \( 15 a^4 \). Then, always factor out any common variables or constants before you divide! It’s like decluttering your room: take out what you don’t need to see the shiny stuff more clearly!