Final Answer:
No, the terms -4xy² and 1/2x²y are not like terms. Like terms have the same variables raised to the same powers, and in this case, the variables are arranged differently and the powers differ, making them unlike terms.
Step-by-step explanation:
Like terms are terms that share the same variables raised to the same powers. In the given terms, -4xy² and 1/2x²y, the variables are x and y, but their arrangement and powers differ. In -4xy², the variable x is multiplied by y², whereas in 1/2x²y, x is squared and multiplied by y. The term 1/2x²y can be rearranged as 1/2yx², and it becomes evident that the arrangement of variables and the powers are not the same as in -4xy². Therefore, they are not like terms.
Understanding like terms is crucial in algebra for simplifying expressions and combining terms. Like terms can be added or subtracted by combining their coefficients while keeping the common variables and powers. In this case, since -4xy² and 1/2x²y are not like terms, they cannot be combined directly. Proper identification and handling of like terms are fundamental skills in algebraic manipulations.