Question

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

Explanation:

Step1: Simplify coefficients and variables separately

For the coefficient: $\frac{4}{3}$ remains as is. For variable \( m \): use the rule \( \frac{a^m}{a^n}=a^{m - n} \), so \( \frac{m^4}{m^2}=m^{4 - 2}=m^2 \).

Step2: Simplify variable \( n \)

Using the same exponent rule, \( \frac{n^3}{n^2}=n^{3 - 2}=n^1 = n \).

Step3: Simplify variable \( p \)

Applying the rule, \( \frac{p^3}{p^4}=p^{3 - 4}=p^{-1}=\frac{1}{p} \).

Step4: Combine all simplified parts

Multiply the simplified coefficient, \( m \), \( n \), and \( p \) parts together: \( \frac{4}{3} \times m^2 \times n \times \frac{1}{p}=\frac{4m^2n}{3p} \).

Answer:

\(\frac{4m^2n}{3p}\)