Prime Factorization can be defined as decomposition of Composite Number into non divisible Numbers. Composite numbers are those numbers which can be further classified. Non divisible numbers are called Prime Numbers that cannot be further decomposed such as 2, 3, 5, etc. Product of prime numbers is equals to composite number. Two methods can be used to obtain the prime factorization of any given number. These are division method and factor Tree method. Let's see how prime factorization of a number with exponents can be obtained. Take 45 and find its prime factorization.

Number 2 cannot be prime factor for 45 since 45 cannot be divided by 2. Let’s try 3 which results in 45 as 3 x 15 = 45.
Thus first factor is ‘3'. Now we have to get factor of 15 which can be 3 and 5 since 3 * 5 = 15.
Since both 3 and 5 are prime factors and cannot be further divided and hence we can write
prime factors of 45 are 3, 3, 5 that is 3 x 3 x 5 = 45.
If we have same factor more than once then they can be written in form of exponents that is 3 is used twice hence it can be written as (3)². So answer can be given as 45 = 3² x 5.
Let’s see what are the prime factorization of 210 bkt using exponents bkt.

Now to factor 210, first break it into two factors such that:
210 ÷ 3 = 70
70 ÷ 2 = 35
35 ÷ 5 = 7
7 ÷ 7 = 1
Thus prime factors for 210 will be 2 * 3 * 5 * 7.