To express the prime factorization of 128 as a product of prime numbers with exponents, we first need to find the prime factors of 128.
128 can be divided by 2 repeatedly:
- \( 128 \div 2 = 64 \)
- \( 64 \div 2 = 32 \)
- \( 32 \div 2 = 16 \)
- \( 16 \div 2 = 8 \)
- \( 8 \div 2 = 4 \)
- \( 4 \div 2 = 2 \)
- \( 2 \div 2 = 1 \)
Since we divided by 2 a total of 7 times, the prime factorization of 128 is:
\[ 128 = 2^7 \]
So, the prime factorization of 128 as a product of prime numbers with exponents is:
\( 2^7 \).