The value of 3 2^4 2^ - 5 2^6 is = ?

Answer: Option B

$$\begin{array}{rl}& \text{root}3\text{of}{2}^4\sqrt{2^{-5}\sqrt{2^6}}\\ & =\text{root}3\text{of}{2}^4\sqrt{2^{-5}{\left(2^6\right)}^{\frac{1}{2}}}\\ & =\text{root}3\text{of}{2}^4\sqrt{2^{-5}{\left(2\right)}^{\left(6\times \frac{1}{2}\right)}}\\ & =\text{root}3\text{of}{2}^4\sqrt{2^{-5}{.2}^3}\\ & =\text{root}3\text{of}{2}^4\sqrt{2^{\left(-5+3\right)}}\\ & =\text{root}3\text{of}{2}^4\sqrt{2^{-2}}\\ & =\text{root}3\text{of}{2}^4.{\left(2^2\right)}^{\frac{1}{2}}\\ & \text{ = }\text{root}3\text{of}{2}^4{.2}^{\left(-2\times \frac{1}{2}\right)}\\ & =\text{root}3\text{of}{2}^4{.2}^{\left(-1\right)}\\ & =\text{root}3\text{of}{2}^{\left(4-1\right)}\\ & \text{ = }\text{root}3\text{of}{2}^3\\ & \text{ = }{\left(2^3\right)}^{\frac{1}{3}}\\ & \text{ = }{\text{2}}^{\left(3\times \frac{1}{3}\right)}\\ & \text{ = 2 }\end{array}$$