Simplify :

−2197−−−−−√3×−125−−−−√3÷27512−−−−√3=?$$\sqrt[3]{-2197}\times \sqrt[3]{-125}÷\sqrt[3]{\frac{27}{512}}=?$$

$$\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, = ?$$

Explanation:-

$$\eqalign{ & \,\,\,\,\,\,\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \, \cr & = \root 3 \of {13 \times 13 \times 13 \times - 1} \times \sqrt {5 \times 5 \times 5 \times - 1} \div \root 3 \of {\frac{{27}}{{512}}} \cr & = \left( {13 \times 5\root 3 \of { - 1 \times - 1} } \right) \div \frac{3}{8} \cr & = 13 \times 5 \times \frac{8}{3} \cr & = \frac{{520}}{3} \cr}$$