Simplify: \(\left(\frac{x^{-4}}{y^{-10}}\right)^{5/4}\)
Solution
\[ \left(\frac{x^{-4}}{y^{-10}}\right)^{5/4} \]
\[ = (x^{-4} \cdot y^{10})^{5/4} \]
\[ = x^{-4 \cdot \frac{5}{4}} \cdot y^{10 \cdot \frac{5}{4}} \]
\[ = x^{-5} \cdot y^{25/2} \]
\[ = \frac{y^{25/2}}{x^5} \]
Final Answer:
\[ \boxed{\frac{y^{25/2}}{x^5}} \]