Final answer:
The pattern in the numbers is that each number can be expressed as the product of a base number raised to a certain power. Maria can fit 1,000 1-cubic-inch cubes inside the box.
Step-by-step explanation:
The pattern in the numbers provided is that each number can be expressed as the product of a base number raised to a certain power. For example, 1 can be expressed as 1 × 1 (1 raised to the power of 1) and 1 × 1 × 1 (1 raised to the power of 3). Similarly, 64 can be expressed as 8 × 8 (8 raised to the power of 2) and 4 × 4 × 4 (4 raised to the power of 3). This pattern continues for each number provided.
Now, let's move on to the second part of the question about fitting 1,000 1-cubic-inch cubes inside a cube-shaped box that measures 9 inches along each edge.
To find out if Maria can fit 1,000 1-cubic-inch cubes inside the box, we need to calculate the volume of the box and the volume of each cube.
The volume of the box can be calculated using the formula V = s^3, where s is the length of one side of the cube. In this case, the length of one side is 9 inches. So, the volume of the box is 9^3 = 729 cubic inches.
The volume of each cube is 1 cubic inch.
To see if Maria can fit 1,000 1-cubic-inch cubes inside the box, we divide the volume of the box by the volume of each cube: 729 / 1 = 729.
Since 729 is less than 1,000, Maria can fit 1,000 1-cubic-inch cubes inside the box.