4. \( (x y)^{3} \div(x y)^{2} \)

To simplify \( (x y)^{3} \div (x y)^{2} \), you can use the property of exponents which states that \( \frac{a^m}{a^n} = a^{m-n} \). Here, you have: \[ (x y)^{3 - 2} = (x y)^{1} = x y. \] So, the simplified expression is \( x y \). To further understand exponents in this context, it’s helpful to remember that they're just shorthand for repeated multiplication. For instance, \( (x y)^{3} \) means \( (x y) \cdot (x y) \cdot (x y) \). When you divided by \( (x y)^{2} \), you're essentially canceling out two of those factors, leaving you with just one \( (x y) \)! If you want to dive deeper, a classic example of similar exponent rules can be found in algebra texts that cover polynomials and functions. Books like "Algebra and Trigonometry" by Michael Sullivan provide excellent examples and practice problems that could solidify your understanding of operations with exponents.