What is the value of (5^2) × (5^(-3))?

The value of (5^2) × (5^(-3)) is 1/5.

To understand why this is the case, let's break it down step by step. When you multiply powers of the same base, you add the exponents. This is a fundamental rule of indices (or exponents). In this case, the base is 5, and we have the exponents 2 and -3.

So, we start with the expression (5^2) × (5^(-3)). According to the rule of indices, we add the exponents together:

5^(2 + (-3)) = 5^(2 - 3) = 5^(-1).

Now, 5^(-1) means 1 divided by 5, which is written as 1/5. This is because a negative exponent indicates the reciprocal of the base raised to the positive exponent. In simpler terms, 5^(-1) is the same as 1/(5^1), which simplifies to 1/5.

So, the value of (5^2) × (5^(-3)) is indeed 1/5. This example illustrates how understanding the rules of indices can simplify seemingly complex expressions. Remember, when multiplying powers with the same base, just add the exponents, and if you end up with a negative exponent, it means you take the reciprocal of the base raised to the positive exponent.