\(Use:\\\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\(a^n)^m=a^{n\cdot m}\\\\(a\cdot b)^n=a^nb^n\\\\a^{-n}=\dfrac{1}{a^n}\)
\(\left(\dfrac{x^3}{2y^6}\right)^{-3}=\dfrac{(x^3)^{-3}}{(2y^6)^{-3}}=\dfrac{x^{3\cdot(-3)}}{2^{-3}(y^6)^{-3}}=\dfrac{x^{-9}}{\frac{1}{2^3}y^{6\cdot(-3)}}\)
\(=\dfrac{x^{-9}}{\frac{1}{8}y^{-18}}=\dfrac{\frac{1}{x^9}}{\frac{1}{8y^{18}}}=\dfrac{1}{x^9}:\dfrac{1}{8y^{18}}=\dfrac{1}{x^9}\cdot\dfrac{8y^{18}}{1}=\boxed{\frac{8y^{18}}{x^9}}\)
