Which statement is correct for (x^2y) and (xy^2)?

Correct answer: They are unlike terms because powers are different

Two algebraic terms are like terms only when the exponent of every corresponding variable is the same. In \(x^2y\), x has exponent 2 and y has exponent 1. In \(xy^2\), x has exponent 1 and y has exponent 2. Although both terms contain the same two variables, their powers do not match. Therefore they are unlike terms, so option B is correct.

The order of writing the variables is not the real issue; the exponents attached to each variable must be compared. For instance, \(4x^2y\) and \(-7x^2y\) would be like terms because both have the pattern \(x^2y\). But \(x^2y\) and \(xy^2\) have different variable parts and cannot be combined by ordinary addition. They are not constants, and multiplying their variable parts is not what the question asks. Hence B is the correct statement.