c. \( \left(\frac{x^{4}}{y}\right)^{2} \)

To simplify the expression \( \left(\frac{x^{4}}{y}\right)^{2} \), we can use the power of a quotient property, which states that \( \left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}} \). Applying this rule gives us \( \frac{(x^{4})^{2}}{y^{2}} \). Now, we can simplify \( (x^{4})^{2} \) using the power of a power property, resulting in \( x^{8} \). Thus, the expression simplifies to \( \frac{x^{8}}{y^{2}} \). Additionally, remember to keep an eye on the inequalities between powers when working with variables. For instance, if you later encounter conditions for \(x\) and \(y\), those will dictate how you can further manipulate or simplify your expressions, especially when combining them in more complex equations.