1. **State the problem:** We need to find the area $A$ of a square with side length $s = 4m^2n^4$. 2. **Formula:** The area of a square is given by the formula: $$A = s^2$$ 3. **Substitute the given side length:** $$A = (4m^2n^4)^2$$ 4. **Apply the power to each factor:** $$A = 4^2 \times (m^2)^2 \times (n^4)^2$$ 5. **Simplify each term:** $$A = 16 \times m^{2 \times 2} \times n^{4 \times 2}$$ 6. **Final simplified expression:** $$A = 16m^4n^8$$ **Answer:** The area of the square is $16m^4n^8$.