Simplify : $$\root 3 \of { - 2197} \,\times $$ $$\root 3 \of { - 125} \,\,\div $$ $$\root 3 \of {\frac{{27}}{{512}}} $$ = ?
A. $$\frac{{492}}{7}$$
B. $$\frac{{520}}{3}$$
C. $$\frac{{554}}{7}$$
D. $$\frac{{571}}{5}$$
Answer: Option B
Solution(By Examveda Team)
$$\,\,\,\,\,\,\root 3 \of { - 2197} \times \root 3 \of { - 125} \div \root 3 \of {\frac{{27}}{{512}}} \,$$$$ = \root 3 \of {13 \times 13 \times 13 \times - 1} \,\, \times $$ $$\sqrt {5 \times 5 \times 5 \times - 1} \,\,\div $$ $$\root 3 \of {\frac{{27}}{{512}}} $$
$$\eqalign{ & = \left( {13 \times 5\root 3 \of { - 1 \times - 1} } \right) \div \frac{3}{8} \cr & = 13 \times 5 \times \frac{8}{3} \cr & = \frac{{520}}{3} \cr} $$
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