Question

1. \\(\frac{m^3 p^4 q^4}{2 m p q}\\)

Explanation:

Step1: Simplify \( m \) terms

For the variable \( m \), use the exponent rule \( \frac{a^m}{a^n}=a^{m - n} \). Here, \( \frac{m^3}{m}=m^{3 - 1}=m^2 \).

Step2: Simplify \( p \) terms

For the variable \( p \), apply the same exponent rule. \( \frac{p^4}{p}=p^{4 - 1}=p^3 \).

Step3: Simplify \( q \) terms

For the variable \( q \), use the exponent rule. \( \frac{q^4}{q}=q^{4 - 1}=q^3 \).

Step4: Combine results

The coefficient remains \( \frac{1}{2} \), and we combine the simplified variable terms. So the simplified form is \( \frac{m^2p^3q^3}{2} \).

Answer:

\(\frac{m^{2}p^{3}q^{3}}{2}\)