Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 19

$\dfrac{-a^{6}}{512y^{9}x^{3}}$

Using laws of exponents, the given expression simpifies to \begin{align*} & (-8y^3xa^{-2})^{-3} \\&= -8^{-3}y^{3(-3)}x^{-3}a^{(-2)(-3)} \\&= -8^{-3}y^{-9}x^{-3}a^{6} \\\\&= \dfrac{-a^{6}}{8^{3}y^{9}x^{3}} \\\\&= \dfrac{-a^{6}}{512y^{9}x^{3}} .\end{align*}