1. **State the problem:** Simplify the expression $$2k (k^3)^3$$. 2. **Recall the exponent rules:** - Power of a power: $$(a^m)^n = a^{mn}$$ - Product of powers: $$a^m \cdot a^n = a^{m+n}$$ 3. **Apply the power of a power rule:** $$(k^3)^3 = k^{3 \times 3} = k^9$$ 4. **Rewrite the expression:** $$2k \cdot k^9$$ 5. **Apply the product of powers rule:** $$k^1 \cdot k^9 = k^{1+9} = k^{10}$$ 6. **Final simplified expression:** $$2k^{10}$$ Therefore, the simplified form of $$2k (k^3)^3$$ is $$2k^{10}$$.