Answer:
No, -4xy^2 and 1/2 x^2y are not like terms.
Explanation:
Like terms are terms that have the same variables with the same exponents. In this case, -4xy^2 and 1/2 x^2y do not have the same variables with the same exponents, so they are not like terms.
-4xy^2 has a coefficient of -4, a variable x, and an exponent of y^2. 1/2 x^2y has a coefficient of 1/2, a variable x, and an exponent of x^2y. Since the variables and exponents are not the same, these terms are not like terms.
To combine like terms, you must add or subtract the coefficients of the terms and keep the variables and exponents the same. In this case, you cannot combine -4xy^2 and 1/2 x^2y because they are not like terms.