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

Solution (By Examveda Team)

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