1. **Problem:** Simplify the expression $\frac{1}{8}x \cdot x - \frac{3}{2}$.\n2. Use the exponent rule $x \cdot x = x^2$.\n$$\frac{1}{8}x \cdot x - \frac{3}{2} = \frac{1}{8}x^2 - \frac{3}{2}$$\n3. The expression is already simplified because there are no like terms to combine.\n4. **Final answer:** $\frac{1}{8}x^2 - \frac{3}{2}$