Final answer:
The student's question demonstrates raising a fraction to a power in mathematics, specifically (5/8)^2 which results in 25/64.
Step-by-step explanation:
The equation 5 over 8 to the power of 2 equals 25 over 64 is an example of exponential notation in mathematics. When we raise a fraction to a power, we raise both the numerator and the denominator of the fraction to that power. Thus, taking (5/8)^2 involves squaring 5 to get 25, and squaring 8 to get 64, resulting in the fraction 25/64. This is a clear demonstration of the rules of exponents, which state that when a base is raised to a power, every component of the base must be raised to that power.
Let's look at another example: if we have (3/4)^2, we square the numerator 3 to get 9, and square the denominator 4 to get 16, giving us the fraction 9/16 as the result. Understanding these principles is crucial for solving problems involving powers and roots, and can also help with simplification and calculation of more complex expressions.
It's important to note that there are many ways to reach the same mathematical result, which can help in verifying the correctness of your work. Whether you are multiplying exponents, adding powers of ten, or working with reciprocals, applying the fundamental principles consistently will lead to the desired outcome.