Final answer:
The prime factorization of 36 using exponential notation is 2² · 3², which shows the number 36 can be broken down into the prime numbers 2 and 3, each raised to the power of 2.
Step-by-step explanation:
The question asks for the prime factorization of 36 using exponential notation. To factor a number into its prime factors, we break it down into the set of prime numbers that, when multiplied together, result in the original number. For the number 36, we start by dividing it by the smallest prime number, which is 2. We get 36 divided by 2 equal to 18. We can divide 18 by 2 again, which gives us 9. Now, 9 is not divisible by 2, but it is divisible by 3. Dividing 9 by 3, we get 3, which is also a prime number. Therefore, 36 can be broken down into 2 x 2 x 3 x 3, which can be written using exponential notation as 2² · 3².