Final answer:
To simplify the expression 2^5/2^a = 2^b = c, use the properties of exponents to subtract the power of the denominator from the power of the numerator.
Step-by-step explanation:
Simplifying Exponential Expressions
To simplify the expression 25/2a, we can use the rule of exponents that states when dividing exponential expressions with the same base, we subtract the exponents. So, 25/2a = 25-a. Therefore, if 25-a is equal to 2b then b must be equal to 5-a. In order to find the value of c, which is 2b, we first need to determine the value of a to express b in terms of a known number and then calculate 2b to find c.
If we are given a specific value for a, we can then simplify the expression completely. For example, if a is 2, then b is 3 (since 5 - 2 = 3), and c would be 23 or 8. Understanding the properties of exponents is crucial in solving problems like this efficiently and correctly.