The value of $$\left(5\frac{1}{4}\div\frac{3}{7}  of  \frac{1}{2}\right)\times \left(5\frac{1}{4}\times\frac{3}{7} \div\frac{1}{2}\right)\div \left(5\frac{1}{4}\div\frac{3}{7}\times \frac{1}{2}\right)$$ is 

$$=\left(\frac{21}{4}\div\frac{3}{14}\right)\times\left(\frac{21}{4}\times\frac{3}{7}\times2\right)\div\left(\frac{21}{4}\times\ \frac{7}{3}\times\frac{1}{2}\right)$$

$$=\left(\frac{21}{4}\times\frac{14}{3}\right)\times\left(\frac{9}{2}\right)\div\left(\frac{49}{8}\right)$$

$$=\left(\frac{7}{2}\times\frac{7}{1}\right)\times\left(\frac{9}{2}\right)\div\left(\frac{49}{8}\right)$$

$$=\left(\frac{49}{2}\right)\times\left(\left(\frac{9}{2}\right)\times\ \left(\frac{8}{49}\right)\right)$$

$$=9\times\ 2$$

= 18