a. \( \left(\frac{a}{b^{2}}\right)^{3} \)

When you raise a fraction to a power, you raise both the numerator and the denominator to that power. So in this expression, you take \(a\) to the power of 3, which gives you \(a^{3}\), and you take \(b^{2}\) to the power of 3 as well, resulting in \(b^{6}\). Therefore, the expression simplifies to \( \frac{a^{3}}{b^{6}} \). And did you know that exponent rules can be applied in many real-world scenarios? For instance, in computer science, algorithms often use similar mathematical principles to analyze complex problems, optimizing performance by comparing their time and space complexities, which can involve exponential functions!