Question

1. \\(\frac{8}{5x} \cdot \frac{4}{11x^2}\\)

Explanation:

Step1: Multiply numerators and denominators

To multiply two fractions, we multiply the numerators together and the denominators together. So for \(\frac{8}{5x} \cdot \frac{4}{11x^2}\), we have \(\frac{8 \times 4}{5x \times 11x^2}\).

Step2: Simplify the products

Calculate the product of the numerators: \(8\times4 = 32\). Calculate the product of the denominators: \(5x\times11x^2=5\times11\times x\times x^2 = 55x^{1 + 2}=55x^3\) (using the rule of exponents \(a^m\times a^n=a^{m + n}\)). So the result is \(\frac{32}{55x^3}\).

Answer:

\(\frac{32}{55x^3}\)