Final answer:
The prime factorization of 36 is 222. This uses the concept that in multiplication of exponentials, we add the exponents when the bases are the same.
Step-by-step explanation:
To write the prime factorization of 36, we start by finding the prime numbers that multiply together to give 36. Breaking it down, we find that 36 can be divided evenly by 2, which gives us 2 × 18. Then we take the number 18 and find that it can be divided evenly by 2 as well, giving us another factor of 2 and a quotient of 9. The number 9 can be divided evenly by 3, giving us 3 × 3. Therefore, we can express 36 as the product of prime factors: 2 × 2 × 3 × 3. Using exponents to simplify, we write this as 22× 32.
Exponents denote how many times a number is multiplied by itself. In multiplication of exponentials, we simply add the exponents when the bases are the same, which is helpful in finding the prime factorization and simplifying expressions.