1. **Stating the problem:** Simplify the expression $$4^3 \sqrt{3}$$. 2. **Recall the rules:** - The cube power means $$4^3 = 4 \times 4 \times 4$$. - The square root $$\sqrt{3}$$ means the number which when squared gives 3. - We cannot simplify $$\sqrt{3}$$ further since 3 is not a perfect square. 3. **Calculate the cube:** $$4^3 = 4 \times 4 \times 4 = 64$$ 4. **Rewrite the expression:** $$4^3 \sqrt{3} = 64 \sqrt{3}$$ 5. **Final answer:** The simplified form is $$64 \sqrt{3}$$. This is the simplest form because $$\sqrt{3}$$ cannot be simplified further.