Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 408: 39

$-\dfrac{4}{x^4}$

Using the laws of exponents, the given expression, $ \dfrac{-8x^3}{2x^7} ,$ simplifies to \begin{array}{l}\require{cancel} (-8\div2)x^{3-7} \\\\= -4x^{-4} \\\\= \dfrac{-4}{x^4} \\\\= -\dfrac{4}{x^4} .\end{array}