What does (xy) to the power of a equal?

The expression ((xy)^a) can be expanded using the properties of exponents. The key property here states that when you have a product raised to an exponent, you can distribute that exponent to each factor in the product. Specifically, ((xy)^a = x^a \cdot y^a).

This means you take the base (x) and raise it to the power of (a), and then you take the base (y) and also raise it to the power of (a), ultimately multiplying the two results together. Thus, ((xy)^a) simplifies neatly to (x^a \cdot y^a).

Understanding this rule is fundamental in algebra, as it applies not only to single variables but also to more complex expressions involving products of terms. It ensures that students can manipulate equations correctly when they encounter exponential expressions in more advanced mathematics. Therefore, the correct choice reflects this essential property of exponents.