1. **State the problem:** Simplify the expression $$- \frac{1}{2} n^2 \times - \frac{1}{2} n^6 \times n^7$$. 2. **Recall the rules:** When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Multiply the coefficients:** $$- \frac{1}{2} \times - \frac{1}{2} = \frac{1}{4}$$ because negative times negative is positive. 4. **Add the exponents of $$n$$:** $$2 + 6 + 7 = 15$$. 5. **Combine the results:** $$\frac{1}{4} n^{15}$$. **Final answer:** $$\frac{1}{4} n^{15}$$.