Express the prime factorization of 128 as a product of prime numbers with exponents.
To find the prime factorization of 128, we start by dividing by the smallest prime number, which is 2.
128 ÷ 2 = 64
We continue dividing by 2 until we can no longer do so:
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
After dividing by 2 six times, we are left with 2. Now that we cannot divide further by 2, we move on to the next prime number, which is 3. However, 128 is not divisible by 3.
Therefore, the prime factorization of 128 is 2 × 2 × 2 × 2 × 2 × 2, which can be written as 2^7.