1. **State the problem:** We need to find the square of the fraction $\frac{3}{2}$. 2. **Formula:** To square a fraction, square the numerator and the denominator separately: $$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$ 3. **Apply the formula:** $$\left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2}$$ 4. **Calculate powers:** $$\frac{3^2}{2^2} = \frac{9}{4}$$ 5. **Final answer:** The square of $\frac{3}{2}$ is $\frac{9}{4}$.