Find the value of m for which it satisfies $$\left( \frac{21}{8} \right)^{12} \times \left( \frac{8}{21} \right)^{14} \times \left( \frac{21}{8} \right)^{14} = \left( \frac{8}{21} \right)^{9m+20}$$​

Correct option is B

Given: ​

​$$\left( \frac{21}{8} \right)^{12} \times \left( \frac{8}{21} \right)^{14} \times \left( \frac{21}{8} \right)^{14} = \left( \frac{8}{21} \right)^{9m+20}$$ 

Formula Used: ​

​$$\frac1{a^m} = a^{-m} \\ \ \\ a^m\times a^n = a^{m+n}$$​​
Solution: ​

​$$\left( \frac{21}{8} \right)^{12} \times \left( \frac{8}{21} \right)^{14} \times \left( \frac{21}{8} \right)^{14} = \left( \frac{8}{21} \right)^{9m+20}\\ \ \\ \left( \frac{8}{21} \right)^{-12} \times \left( \frac{8}{21} \right)^{14} \times \left( \frac{8} {21}\right)^{-14} = \left( \frac{8}{21} \right)^{9m+20} \\ \ \\ \left( \frac{8}{21} \right)^{(-12)+14-14}=\left( \frac{8}{21} \right)^{9m+20} \\ \ \ \\ \implies-12 = 9m+20 \\ \ \\ 9m = -12-20 =-32 \\ \ \\ m = \frac{-32}{9}$$​​