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 = \(\frac{30}{24} = \frac{5}{4}\)