**The prime factorization of 72 is 2 ^{3x} 3^{2}, or 2 x 2 x 2 x 3 x 3.** The prime factorization of a number involves determining the factors of a number that are also prime numbers and multiply together to equal the original number.

To determine the prime factorization of 72, the number should be broken down one step at a time by the lowest factor available, which in this case is 2: 72 = 36 x 2. Since 36 is not a prime number, the process should be repeated until all prime numbers are obtained: 36/2 = 18 x 2. Continuing on, 18/2 = 9, and 9/3 = 3. Combining all of the prime factors together, 72 is equal to 2 x 2 x 2 x 3 x 3.