a) \( \frac{2}{x^{3}} \cdot \frac{3 x^{2}}{8} \)

To simplify \( \frac{2}{x^{3}} \cdot \frac{3 x^{2}}{8} \), start by multiplying numerators and denominators. The numerator becomes \( 2 \cdot 3 x^{2} = 6 x^{2} \) and the denominator is \( x^{3} \cdot 8 = 8 x^{3} \). So, we have \( \frac{6x^{2}}{8x^{3}} \). Next, simplify the fraction: \( \frac{6}{8} = \frac{3}{4} \) and reduce the x terms \( \frac{x^{2}}{x^{3}} = \frac{1}{x} \). Therefore, the final expression is \( \frac{3}{4x} \). In mathematical expressions like these, it's crucial to keep track of each factor. A common mistake is to forget to simplify fractions fully or mismanage the exponents while dividing terms. Always double-check your calculations and simplify step by step!