1. **State the problem:** Simplify the expression $x^4 \div 2$. 2. **Formula and rules:** Division by a number means dividing the coefficient or constant part of the expression by that number. Since $x^4$ means $x$ raised to the power 4, and there is no coefficient explicitly written, it is understood as $1 \cdot x^4$. 3. **Intermediate work:** $$x^4 \div 2 = \frac{x^4}{2}$$ 4. **Explanation:** We simply place $x^4$ over 2 as a fraction. This is the simplest form since $x^4$ cannot be divided by 2 further. 5. **Final answer:** $$\frac{x^4}{2}$$