Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 409: 59

$-\dfrac{y^{3}}{8}$

Using the laws of exponents, the given expression, $ \left( -2y^{-1} \right)^{-3} ,$ simplifies to \begin{array}{l}\require{cancel} (-2)^{1(-3)}y^{-1(-3)} \\\\= (-2)^{-3}y^{3} \\\\= \dfrac{y^{3}}{(-2)^{3}} \\\\= \dfrac{y^{3}}{-8} \\\\= -\dfrac{y^{3}}{8} .\end{array}