Final answer:
The area of the rectangle is (3^6 * 9^2) inches^2, and the area of the square is (9^3)^2 inches^2. Simplifying the expressions, we find that the areas of the two figures are equal.
Step-by-step explanation:
The area of a rectangle is equal to its length multiplied by its width. So, the area of the rectangle can be found by multiplying the length (3^6 inches) by the width (9^2 inches). The area of the rectangle is (3^6 inches) * (9^2 inches) = 3^6 * 9^2 inches^2.The area of a square is equal to the side length squared. So, the area of the square with a side length of 9^3 inches is (9^3 inches)^2 = (9^3)^2 inches^2.
To compare the areas, we can simplify the expressions for both figures. The area of the rectangle is 3^6 * 9^2 inches^2, which can be simplified to (3^2 * 9^2)^3 inches^2. The area of the square is (9^3)^2 inches^2, which simplifies to 9^6 inches^2.Comparing the simplified expressions, we can see that (3^2 * 9^2)^3 is equal to 9^6. This means that the areas of the two figures are equal.