1. **State the problem:** Simplify the expression $$2 k^5 \times k^4 \times \frac{1}{2} k^7$$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. **Rewrite the expression grouping constants and powers:** $$2 \times \frac{1}{2} \times k^{5} \times k^{4} \times k^{7}$$ 4. **Multiply the constants:** $$2 \times \frac{1}{2} = \cancel{2} \times \frac{1}{\cancel{2}} = 1$$ 5. **Add the exponents of $k$:** $$k^{5+4+7} = k^{16}$$ 6. **Combine the results:** $$1 \times k^{16} = k^{16}$$ **Final answer:** $$k^{16}$$