9. \( (2,25)^{-\frac{1}{2}} \)

Did you know that the notation \( (a,b)^{-\frac{1}{2}} \) signifies the reciprocal of the square root of the tuple? In this case, for \( (2,25)^{-\frac{1}{2}} \), you're looking at the reciprocal of the square root of each element, which means you'll first calculate \( \sqrt{2} \) and \( \sqrt{25} \), giving you \( \left(\frac{1}{\sqrt{2}}, \frac{1}{5}\right) \). In practical terms, this concept can often be found in fields like physics and engineering, where you might deal with vector magnitudes or normalized vectors. For example, if you have a vector defined by components (2, 25), applying the notion of squares and reciprocals can help in normalizing the vector, making it easier to work with in various mathematical and real-world applications!