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

The value of (5^3)/(5^2) is 5.

To understand why this is the case, let's break down the problem using the rules of indices (or exponents). When you divide two numbers with the same base, you subtract the exponent of the denominator from the exponent of the numerator. In this case, both the numerator and the denominator have the base 5. The numerator is 5^3, which means 5 raised to the power of 3, and the denominator is 5^2, which means 5 raised to the power of 2.

Using the rule of indices for division, we get:
(5^3)/(5^2) = 5^(3-2) = 5^1.

Since any number raised to the power of 1 is the number itself, 5^1 is simply 5.

To visualise this, consider what 5^3 and 5^2 represent. 5^3 is 5 * 5 * 5, and 5^2 is 5 * 5. When you divide 5 * 5 * 5 by 5 * 5, you can cancel out two 5s from the numerator and the denominator, leaving you with just one 5. This confirms that (5^3)/(5^2) simplifies to 5.

Understanding these rules helps simplify many problems involving indices and makes calculations much easier. Keep practising these rules, and you'll find that working with exponents becomes second nature!