Final answer:
The width of the rectangle is calculated by dividing the area by the length. Using the formula Width = Area ÷ Length and substituting the given values, the width is found to be 8x^3y^2 yards.
Step-by-step explanation:
To find the width of the rectangle, we need to use the formula for the area of a rectangle, which is Area = Length × Width. We are given the area and the length, so we can rearrange the formula to solve for the width as follows: Width = Area ÷ Length.
Substituting the given values into this formula, we get:
Width = (64x^8y^5) ÷ (8x^5y^3)
Now, divide the coefficients (numbers) and the variables separately using the laws of exponents:
Width = (64 ÷ 8) × (x^8 ÷ x^5) × (y^5 ÷ y^3)
Width = 8 × x^(8-5) × y^(5-3)
Width = 8 × x^3 × y^2
Therefore, the width of the rectangle is 8x^3y^2 yards.