Final answer:
To determine the width shared by all three fields, we find the greatest common factor in the algebraic expressions for the area of each field, which is xy. The greatest width is assumed to be represented by this term as it is the common factor with the lowest powers in all expressions.
Step-by-step explanation:
The student is asking about the widths of three rectangular fields with given areas expressed as algebraic expressions. To find the common width shared by all fields when the areas are 14x⁴y, 6xy³, and 10xy, we need to identify the common factors between these expressions. Since the fields are rectangular and the areas are determined by the product of length and width, the common factor in the algebraic expressions is presumably the width.
Without additional information, such as the exact dimensions or additional relationships between the lengths and widths, we cannot determine a numerical value for the width. However, the farmer is interested in finding the greatest width, which would be the highest common power of x or y across all three expressions. In this case, the greatest width is indicated by the term with the lowest powers of x and y present in all expressions, which is xy.