Simplify: \((\sqrt{x^{-3}})^5\)
Solution
\[ (\sqrt{x^{-3}})^5 \]
\[ = \left((x^{-3})^{1/2}\right)^5 \]
\[ = (x^{-3})^{5/2} \]
\[ = x^{-15/2} \]
\[ = \frac{1}{x^{15/2}} \]
Final Answer:
\[ \boxed{\frac{1}{x^{15/2}}} \]
\[ (\sqrt{x^{-3}})^5 \]
\[ = \left((x^{-3})^{1/2}\right)^5 \]
\[ = (x^{-3})^{5/2} \]
\[ = x^{-15/2} \]
\[ = \frac{1}{x^{15/2}} \]
\[ \boxed{\frac{1}{x^{15/2}}} \]