Exponents and fractions Evaluate. Write your answer as a fraction in simplest form. \( \left(\frac{5}{6}\right)^{2} \)

To evaluate \( \left(\frac{5}{6}\right)^{2} \), you square both the numerator and the denominator. This means you multiply \( 5 \) by itself and \( 6 \) by itself: \[ \left(\frac{5}{6}\right)^{2} = \frac{5^2}{6^2} = \frac{25}{36} \] This fraction is already in its simplest form, so the answer is \( \frac{25}{36} \). In the realm of mathematics, exponents can often look intimidating, but they’re simply shorthand for repeated multiplication. When you raise a fraction to a power, you're just extending the same principle to both the numerator and the denominator. It’s like giving your fraction a little boost, allowing it to grow even more! Understanding exponents is crucial for solving a myriad of real-world problems, especially in fields like finance, computing, and science. For instance, when dealing with compound interest, the formula incorporates exponents to calculate how your money grows over time. Knowing how to manipulate fractions with exponents will make your calculations smoother and help you apply these concepts effectively in practical situations.