Questions: Which of the following terms are like terms? (a) 6xy (b) -2x^3yx^-1 (c) 2x^3x^-2y (d) 6xxx^-1y^3y^-1

Solution Steps

First, we need to simplify each term to identify like terms.

• Term (a): \(6xy\) is already simplified.
• Term (b): \(-2x^{3}yx^{-1}\) simplifies to \(-2x^{3-1}y = -2x^{2}y\).
• Term (c): \(2x^{3}x^{-2}y\) simplifies to \(2x^{3-2}y = 2xy\).
• Term (d): \(6xx^{-1}y^{3}y^{-1}\) simplifies to \(6x^{1-1}y^{3-1} = 6y^{2}\).

Like terms are terms that have the same variables raised to the same powers.

• Term (a): \(6xy\)
• Term (b): \(-2x^{2}y\)
• Term (c): \(2xy\)
• Term (d): \(6y^{2}\)

From the simplifications, we can see that terms (a) and (c) are like terms because they both have the variable \(xy\).

Final Answer