Question

apply geometry
a square floor has a side length of (8x^3y^2) units. a square tile has a side length of (xy) units. how many tiles will it take to cover the floor?

Explanation:

Step1: Find area of floor

The floor is a square with side length \( 8x^3y^2 \). The area of a square is side length squared, so:
\( (8x^3y^2)^2 = 8^2 \times (x^3)^2 \times (y^2)^2 = 64x^6y^4 \)

Step2: Find area of tile

The tile is a square with side length \( xy \). The area of the tile is:
\( (xy)^2 = x^2y^2 \)

Step3: Divide floor area by tile area

To find the number of tiles, divide the area of the floor by the area of one tile:
\( \frac{64x^6y^4}{x^2y^2} = 64x^{6 - 2}y^{4 - 2} = 64x^4y^2 \)

Answer:

\( 64x^4y^2 \)