a \( \left(\frac{3}{2}\right)^{-2}= \)

To solve \( \left(\frac{3}{2}\right)^{-2} \), remember that a negative exponent means you take the reciprocal. Thus, \( \left(\frac{3}{2}\right)^{-2} = \left(\frac{2}{3}\right)^{2} \). Then, squaring \( \frac{2}{3} \) gives you \( \frac{4}{9} \). So, the answer is \( \frac{4}{9} \)! This rule about negative exponents is incredibly handy in simplifying expressions. It’s like a secret shortcut that saves time and effort in math, so be sure to keep it in your toolbox for future problems!