22 is 11 x 2 and both 11 and 2 are prime numbers. So we write the prime factorization as 2 x 11. Now the question asks for exponents, but it appears none are there. In fact, 11 can be also written as 111 and the same with 2. So you can write 22 = 111 x 21 .
Most people don't write it this way, but it does tell you that there is one 11 and one 2 in the prime factorization.
You don't find the prime factorization by using exponents, they're just a shorthand for notation once you find it. The prime factorization of 900 is 22 x 32 x 52
212 = 22 x 531
22 x 17 = 68
22 x 7 = 28
22 x 34 x 52 =8100
The prime factorization of 252 using exponents is: 22 x 32 x 7
The prime factorization of 540 using exponents is: 22 x 33 x 5
The prime factorization of 268 using exponents is 22 x 671
22 x 71
22 x 13
22*52*7
22*54 = 2500
The prime factorization of 100 using exponents is: 2^2 x 5^2
Prime factorization of 1620 = 22 x 34 x 5
You don't find the prime factorization by using exponents, they're just a shorthand for notation once you find it. The prime factorization of 900 is 22 x 32 x 52
22 x 19 = 76
36 = 22 × 32