1. Simplify \( (4 x y)^{2} \)

To simplify \( (4xy)^{2} \), you apply the exponent to both the coefficient and the variables. So, \( (4xy)^{2} = 4^{2} \cdot x^{2} \cdot y^{2} \). That gives you \( 16 \cdot x^{2} \cdot y^{2} \). Therefore, the simplified expression is \( 16x^{2}y^{2} \). Now you've unleashed the full power of exponents in your expression! Remember, when you raise a product to a power, you can separate the factors and simplify each one, which makes calculations a breeze. It's like having superpowers in math!