Question

select the correct answer
lena says that (4xy^3) and (-5x^3y) are like terms. is she correct? why or why not?
a. yes, because both terms have a variable with a power of 3 and a power of 1.
b. no, because the same variables are not raised to the same powers
c. yes, because both terms have an (x) and a (y)
d. no, because the two terms do not have the same coefficients
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Explanation:

Step1: Recall like terms definition

Like terms have same variables raised to same powers.

Step2: Analyze \(4xy^3\) and \(-5x^3y\)

In \(4xy^3\), \(x\) has power \(1\), \(y\) has power \(3\). In \(-5x^3y\), \(x\) has power \(3\), \(y\) has power \(1\). Variables' powers differ.

Step3: Evaluate options

• A: Incorrect, powers differ.
• B: Correct, same variables not same powers.
• C: Incorrect, having same variables isn't enough.
• D: Incorrect, coefficients don't matter for like terms.

Answer:

B. No, because the same variables are not raised to the same powers