(11) \( \left(\frac{3 x}{2}\right)^{-2} \times\left(\frac{x}{x}\right)^{2} \)

To simplify the expression \( \left(\frac{3 x}{2}\right)^{-2} \times\left(\frac{x}{x}\right)^{2} \), we first evaluate each part separately. Starting with \( \left(\frac{x}{x}\right)^{2} \), since \( \frac{x}{x} = 1 \) (as long as \( x \neq 0 \)), we have: \[ \left(\frac{x}{x}\right)^{2} = 1^{2} = 1. \] Now, let's tackle \( \left(\frac{3 x}{2}\right)^{-2} \). The negative exponent indicates that we take the reciprocal: \[ \left(\frac{3 x}{2}\right)^{-2} = \frac{1}{\left(\frac{3 x}{2}\right)^{2}}. \] Now we calculate \( \left(\frac{3 x}{2}\right)^{2} \): \[ \left(\frac{3 x}{2}\right)^{2} = \frac{(3 x)^{2}}{2^{2}} = \frac{9 x^{2}}{4}. \] Thus, \[ \left(\frac{3 x}{2}\right)^{-2} = \frac{4}{9 x^{2}}. \] Putting it all back together, we combine the two parts: \[ \frac{4}{9 x^{2}} \times 1 = \frac{4}{9 x^{2}}. \] The final simplified expression is: \[ \frac{4}{9 x^{2}}. \]