Question

1. \\(\frac{11x}{9x^2} \cdot \frac{12x}{4x^2}\\)

Explanation:

Step1: Multiply numerators and denominators

Multiply the numerators \(11x\) and \(12x\) together, and the denominators \(9x^2\) and \(4x^2\) together. So we get \(\frac{11x \cdot 12x}{9x^2 \cdot 4x^2}\).

Step2: Simplify the expression

First, calculate the product in the numerator: \(11x \cdot 12x = 132x^2\). Then, calculate the product in the denominator: \(9x^2 \cdot 4x^2 = 36x^4\). Now our expression is \(\frac{132x^2}{36x^4}\). Next, simplify the coefficients and the variables. The greatest common divisor of 132 and 36 is 12, so divide numerator and denominator by 12: \(\frac{132\div12}{36\div12} = \frac{11}{3}\). For the variables, use the rule of exponents \( \frac{x^m}{x^n}=x^{m - n}\), so \( \frac{x^2}{x^4}=x^{2-4}=x^{-2}=\frac{1}{x^2}\). Multiply the coefficient and the variable part: \(\frac{11}{3}\cdot\frac{1}{x^2}=\frac{11}{3x^2}\).

Answer:

\(\frac{11}{3x^2}\)