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

The value of (2^5) / (2^2) is 8.

To understand why, 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 2. So, you subtract the exponent of the denominator (2) from the exponent of the numerator (5):

2^5 / 2^2 = 2^(5-2) = 2^3.

Now, you need to calculate 2^3. This means you multiply 2 by itself three times:

2 * 2 * 2 = 8.

Therefore, the value of (2^5) / (2^2) is 8.

This method of subtracting exponents when dividing is a fundamental rule in mathematics and is very useful for simplifying expressions involving powers. Remember, this rule only applies when the bases are the same. If the bases were different, you would need to use a different approach. Understanding and applying these rules will help you solve a wide range of problems more efficiently.