The solution to the surd is

Simplification of surds.
In mathematics, Surd is a term that refers to square roots or other roots that cannot be stated exactly as a finite fraction or decimal. Surds are simplified when they are expressed in a more simpler form while preserving their actual value.
In the given question, we have:
![\sqrt[3]{(729)/(-1000x^3y^6)}](https://img.qammunity.org/2018/formulas/mathematics/high-school/tm59nxup7nj1n3j5jfgzigew9g3c0egy1y.png)
First simplify the fraction;
![\sqrt[3]{(729)/(-1000) * (1)/(x^3y^6)}](https://img.qammunity.org/2018/formulas/mathematics/high-school/rxgw9q8lah6mrah0z3xwnp3ha528auqo4h.png)
Taking the cube root.
![(9)/(-10) * \frac{1}{\sqrt[3]{x^3y^6}}](https://img.qammunity.org/2018/formulas/mathematics/high-school/bn1m5cc1q7f5qwf9asqkihxkm055xcas9x.png)

