To find the exponent of 2 that gives 32, let’s break down the number 32 into its prime factors. The prime factorization of 32 is 2 x 2 x 2 x 2 x 2. So we have five 2’s multiplied together to give 32.
In exponential notation, we can write this as 2^5. The base is 2, which is the number being multiplied, and the exponent is 5, which represents the number of times the base is multiplied by itself.
To illustrate this concept further, let’s consider a real-life scenario. Imagine you have 2 apples, and you want to multiply the number of apples by 2 five times. Each time you multiply, you get twice the number of apples you had before.
Starting with 2 apples:
1st multiplication: 2 x 2 = 4 apples
2nd multiplication: 4 x 2 = 8 apples
3rd multiplication: 8 x 2 = 16 apples
4th multiplication: 16 x 2 = 32 apples
So after multiplying 2 by itself five times, we end up with 32 apples. In this scenario, the base is 2 (the number of apples we start with), and the exponent is 5 (the number of times we multiply the base by itself).
The exponent of 2 that gives 32 is 5.