Question

1. \\(\frac{9a^4}{3a} \cdot \frac{11a^2}{9}\\)

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators \(9a^4\) and \(11a^2\), and the denominators \(3a\) and \(9\). So we get \(\frac{9a^4 \cdot 11a^2}{3a \cdot 9}\).

Step2: Simplify coefficients and variables

For coefficients: \(9\times11 = 99\) and \(3\times9 = 27\), so \(\frac{99a^{4 + 2}}{27a}\) (using \(a^m \cdot a^n=a^{m + n}\)). Then simplify \(\frac{99}{27}=\frac{11}{3}\) and \(a^{6-1}=a^5\) (using \(\frac{a^m}{a^n}=a^{m - n}\)). So we have \(\frac{11}{3}a^5\) or \(\frac{11a^5}{3}\).

Answer:

\(\frac{11a^5}{3}\)