1. **State the problem:** Calculate $(-3:2)^2$. Here, the colon ":" is interpreted as division, so the expression is $\left(\frac{-3}{2}\right)^2$. 2. **Formula used:** The square of a fraction $\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$. 3. **Apply the formula:** $$\left(\frac{-3}{2}\right)^2 = \frac{(-3)^2}{2^2}$$ 4. **Calculate numerator and denominator:** $$\frac{9}{4}$$ 5. **Final answer:** $$\frac{9}{4}$$ This means squaring the fraction $-\frac{3}{2}$ results in $\frac{9}{4}$, which is positive because squaring any real number yields a non-negative result.