8\({\frac{x}{2}}\) = \(2^{\frac{3}{8}})(4^{\frac{3}{4}}\))
 applying the laws of indices.
(\(2^{3\times (\frac{x}{2})})  =  (2^{\frac{3}{8}})(2^{2\times (\frac{3}{4})}\))

\(2^{\frac{3x}{2}} = (2^{\frac{3}{8}})(2^{(\frac{3}{2})}\))

\(\frac{3x}{2} = \frac{3}{8} + \frac{3}{2}\)

\(\frac{3x}{2} =  \frac{3 + 12}{8}\)

\(\frac{3x}{2} = \frac{15}{8}\) 

24x = 30

x = \(\frac{30}{24} = \frac{5}{4}\)