[tex]\left( \sqrt{x^{-3}} \right)^5 = \left( \sqrt{ \frac{1}{x^3} } \right)^5= \frac{1}{ (\sqrt{x^3})^5 } = \frac{1}{ \sqrt{x^{15}} } = \frac{1}{x^7 \sqrt{x} } [/tex]
Explanation for the last step:
[tex] \sqrt{x^{15}}= \sqrt{x^{14}*x}= \sqrt{x^{14}}* \sqrt{x} =x^{ \frac{14}{2} }* \sqrt{x} =x^7 \sqrt{x} [/tex]
