Exponents

The prime factorization of 6,048 is 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 7.

We can make the prime factorization a little more compact by writing it with exponents.

Since 2 × 2 × 2 × 2 × 2 = 25, 3 × 3 × 3 = 33, and 7 = 71, we can write the prime factorization of 6,048 as 25 × 33 × 71.

The prime factorization of 7,875 is 3 × 3 × 5 × 5 × 5 × 7, which we can write as 32 × 53 × 71.

If we wanted to compare the prime factorizations of 6,048 and 7,875, we can also write them with zero exponents:

6,048 = 25 × 33 × 50 × 71

7,875 = 20 × 32 × 53 × 71

Any number (other than zero) to the zeroth power equals one, so 20 = 1 and 50 = 1.