1. **State the problem:** We have a square piece of paper with side length $x$ and area $x^2$. It is divided into smaller squares, each with side length $\frac{x}{4}$. We want to find the area of each small square. 2. **Recall the formula for the area of a square:** The area $A$ of a square with side length $s$ is given by: $$A = s^2$$ 3. **Apply the formula to the small squares:** Each small square has side length $\frac{x}{4}$, so its area is: $$\left(\frac{x}{4}\right)^2$$ 4. **Simplify the expression:** $$\left(\frac{x}{4}\right)^2 = \frac{x^2}{\cancel{4^2}} = \frac{x^2}{16}$$ 5. **Interpretation:** The area of each small square is $\frac{x^2}{16}$. **Final answer:** $\boxed{\frac{x^2}{16}}$