To determine whether the terms [tex]\( 4xy^3 \)[/tex] and [tex]\( -5x^3y \)[/tex] are like terms, we need to check if they have the same variables raised to the same powers. Let’s examine each term in detail:
1. The term [tex]\( 4xy^3 \)[/tex]:
- Variables present: [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
- Power of [tex]\( x \)[/tex]: [tex]\( x^1 \)[/tex]
- Power of [tex]\( y \)[/tex]: [tex]\( y^3 \)[/tex]
2. The term [tex]\( -5x^3y \)[/tex]:
- Variables present: [tex]\( x \)[/tex] and [tex]\( y \)[/tex]
- Power of [tex]\( x \)[/tex]: [tex]\( x^3 \)[/tex]
- Power of [tex]\( y \)[/tex]: [tex]\( y^1 \)[/tex]
For two terms to be considered like terms, both must have exactly the same variables raised to exactly the same powers.
In [tex]\( 4xy^3 \)[/tex]:
- [tex]\( x \)[/tex] is raised to the power of 1.
- [tex]\( y \)[/tex] is raised to the power of 3.
In [tex]\( -5x^3y \)[/tex]:
- [tex]\( x \)[/tex] is raised to the power of 3.
- [tex]\( y \)[/tex] is raised to the power of 1.
Since the exponent of [tex]\( x \)[/tex] in [tex]\( 4xy^3 \)[/tex] is 1 and in [tex]\( -5x^3y \)[/tex] is 3, these terms are not like terms because the same variables are not raised to the same powers.
Therefore, Lena is incorrect. The correct answer is:
D. No, because the same variables are not raised to the same powers.
