Final answer:
Mare made a mistake by not correctly applying the laws of exponents, which involves adding exponents when multiplying like bases and properly handling negative exponents.
Step-by-step explanation:
The student, Mare, wrote the expression as -4x³ * 2y⁻².⁵y⁵-x-B = -40x⁵y³, which was incorrect. The mistake lies in the incorrect application of the laws of exponents and possibly a misinterpretation of the problem's context. First, combining the terms with the same base requires adding the exponents when multiplying, and this was not done.
Second, if there are any negative exponents, it means that the base with the negative exponent should be in the denominator when expressed in a simplified form. Third, the constants -x and B (if they are supposed to be variables and not typos) would not simplify with terms involving x and y to result directly in -40x⁵y³.
To correct the expression, we would need a clearer understanding of what the original problem is, including accurate use of multiplication and division of powers and maintaining the integrity of variable terms that do not combine directly with each other. Without additional context, it is challenging to provide the corrected form of the expression exactly.
However, it is important to follow the rules of exponents and algebraic manipulation correctly, and ensure all variables and constants are appropriately accounted for.