Question

select the correct answer.

lena says that \\(4xy^3\\) and \\(-5x^3y\\) are like terms. is she correct? why or why not?

yes, because both terms have a variable with a power of 3 and a power of 1.
yes, because both terms have an \\(x\\) and a \\(y\\).
no, because the same variables are not raised to the same powers.
no, because the two terms do not have the same coefficients.

Explanation:

Identify the variables and exponents in each term

$$
LATEXBLOCK0
$$

Compare the corresponding exponents of the variables

$$
LATEXBLOCK1
$$

Determine if the terms are like terms

$$ \text{Since the same variables are not raised to the same powers, they are not like terms.} $$

Answer:

• (A) Yes, because both terms have a variable with a power of 3 and a power of 1.
• (B) Yes, because both terms have an \(x\) and a \(y\).
• (C) No, because the same variables are not raised to the same powers. (Correct answer)
• (D) No, because the two terms do not have the same coefficients.