Given,

$8^{0.601}\times {64}^{17}=?$

It can also be approximated as

$$\begin{gathered} \begin{array}{l}{\text{8}}^{\text{0.601}}\times {\left(\text{8}\right)}^{\text{2x 1.7 }}\text{=?}\end{array} \\ \begin{array}{l}{\text{= 8}}^{0.60}\times {\left(8\right)}^{3.4}\end{array} \\ \begin{array}{l}{\text{= 8}}^{0.6+3.4}[\because a^m\times a^n=a^{m+n}]\end{array} \\ \begin{array}{l}{\text{= (8)}}^{\text{4}}\end{array} \end{gathered}$$

 = 64×64

 = 4096

Hence, option E is correct.