1. Simplify: \( \left(\frac{x}{y}\right)^{2} \)

To simplify \( \left(\frac{x}{y}\right)^{2} \), you simply square both the numerator and the denominator. This gives you \( \frac{x^{2}}{y^{2}} \). It's like having a cute little fraction that just got a makeover—everything gets a bump up in power while keeping the same base! Now, don't forget that this simplification can be particularly handy in algebraic expressions, equations, or when you're trying to manipulate fractions. Squaring the fraction makes comparisons, solving, and finding common denominators a piece of cake. So, next time you see a fraction that needs squaring, remember this method!