The area of a square is equal to the side length squared. If the side length is doubled, the area of the new square will be four times larger. Therefore, the ratio of the area of the original square to the area of the new square is $\boxed{\frac{1}{4}}$.
2 x * 2 X = 4 x^2
You wrote the expression for the area of the new square correctly as $4x^2$, which is indeed four times the area of the original square. Therefore, the ratio of the area of the original square to the area of the new square is indeed $\boxed{\frac{1}{4}}$.
