Graduate Management Admission Test (GMAT) Practice Test

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Which of the following equations represents the commutative property of multiplication?

xy = yx
x + y = y + x
x^a + x^b = x^(a + b)
x^a * y^b = (x * y)^(a + b)

The correct answer is: xy = yx

The commutative property of multiplication states that the order of the numbers being multiplied does not affect the product. In other words, if you multiply two numbers, switching their positions will yield the same result. The equation that best illustrates this property is represented by $xy = yx$. This equation clearly shows that multiplying $x$ by $y$ results in the same value as multiplying $y$ by $x$. It directly aligns with the definition of the commutative property, emphasizing that the order of multiplication is irrelevant to the outcome. The other equations pertain to different mathematical principles. For example: - The equation for option B illustrates the commutative property of addition, not multiplication. It demonstrates that the order of terms in addition does not change the sum. - Option C is an identity involving addition of exponents, which pertains to the rules of exponents rather than multiplication. - Option D describes a property of exponents representing how to combine powers of products but does not relate to the commutative property. Thus, the equation $xy = yx$ accurately exemplifies the commutative property of multiplication.