Final answer:
The width of the rectangular pasture, given an area of 20x^6y^5 and a length of 5x^3y^4, is 4x^3y.
Step-by-step explanation:
The student is asking about determining the width of a rectangular pasture given the area and the length of the pasture. The area of the rectangle is represented by the algebraic expression 20x⁶y⁵, and the length is given as 5x³y⁴. To find the width, we divide the area by the length. Dividing algebraic expressions involves reducing common factors.
Width = Area / Length
Width = (20x⁶y⁵) / (5x³y⁴)
Width = (20/5)x⁶-³y⁵-⁴
Width = 4x³y
So, the width that the farmer would need to make the pasture is 4x³y.