The simplified value of following is: $$\left( {\frac{3}{{15}}{a^5}{b^6}{c^3} \times \frac{5}{9}a{b^5}{c^4}} \right)$$     $$ ÷ $$ $$\frac{{10}}{{27}}{a^2}b{c^3}$$

A. $$\frac{3}{{10}}a{b^4}{c^3}$$

B. $$\frac{9}{{10}}{a^2}b{c^4}$$

C. $$\frac{3}{{10}}{a^4}{b^{10}}{c^4}$$

D. $$\frac{1}{{10}}{a^4}{b^4}{c^{10}}$$

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & \left( {\frac{3}{{15}}{a^5}{b^6}{c^3} \times \frac{5}{9}a{b^5}{c^4}} \right) \div \frac{{10}}{{27}}{a^2}b{c^3} \cr & \Rightarrow \frac{1}{9}{a^6}{b^{11}}{c^7} \div \frac{{10}}{{27}}{a^2}b{c^3} \cr & \Rightarrow \frac{{\frac{1}{9}{a^6}{b^{11}}{c^7}}}{{\frac{{10}}{{27}}{a^2}b{c^3}}} \cr & \Rightarrow \frac{3}{{10}}{a^4}{b^{10}}{c^4} \cr} $$