( 32 × 10^ - 5 )^ 2 × 64\, ÷ ( 2^16 × 10^ - 4 ) = 10^?

Answer: Option D

$$\begin{array}{rl}& {\left(32\times {10}^{-5}\right)}^2\times 64÷\left(2^{16}\times {10}^{-4}\right)=10^{?}\\ & \Rightarrow {\left(2^5\times {10}^{-5}\right)}^2\times 2^6÷\left(2^{16}\times {10}^{-4}\right)\\ & =10^{?}.....\left[\because {\left(a^m\right)}^n=a^{mn}\right]\\ & \Rightarrow \frac{2^{10}\times {10}^{-10}\times 2^6}{2^{16}\times {10}^{-4}}\\ & =10^{?}.....\left[\because a^m\times a^n=a^{m+n}\right]\\ & \Rightarrow \frac{2^{16}\times {10}^4}{2^{16}\times {10}^{10}}\\ & =10^{?}.....\left[a^{-m}=\frac{1}{a^m}\right]\\ & \Rightarrow 10^{4-10}=10^{?}\\ & \Rightarrow 10^{-6}=10^{?}\\ & \Rightarrow ?=-6\end{array}$$