help me to solve this please

Mmm

Lets see.

$$\\\dfrac{4\times 2^{1/4}\times8^{1/6}}{16^{3/4}}\\\\\\ =\dfrac{2^2\times 2^{1/4}\times(2^3)^{1/6}}{(2^4)^{3/4}}\\\\\\ =\dfrac{2^2\times 2^{1/4}\times 2^{3/6}}{2^{12/4}}\\\\\\ =\dfrac{2^2\times 2^{0.25}\times 2^{0.5}}{2^{3}}\\\\ =2^{2+0.25+0.5-3}\\\\ =2^{-0.25}\\\\ =\frac{1}{2^{1/4}}\\\\ =\frac{1}{\sqrt[4]{2}}$$