Final answer:
The length of the rectangle is found by dividing the area, x^5 y^6, by the width, xy^2. The calculation results in the length being x^4 y^4 inches.
Step-by-step explanation:
The question is asking for the length of a rectangle given that the area is x^5 y^6 square inches and the width is xy^2 inches. To find the length, we divide the area by the width. This is a classic algebraic manipulation problem requiring understanding of how to divide monomials.
The formula for the area of a rectangle is Area = Length × Width.
We have the area (x^5 y^6) and the width (xy^2), so we divide the area by the width to find the length:
Length = Area ÷ Width = x^5 y^6 ÷ xy^2 = x^4 y^4.