To express the prime factorization of 128, we first need to factor it into its prime components.
128 can be broken down as follows:
- Start by dividing by 2 (the smallest prime number):
- \( 128 \div 2 = 64 \)
- Continue dividing by 2:
- \( 64 \div 2 = 32 \)
- \( 32 \div 2 = 16 \)
- \( 16 \div 2 = 8 \)
- \( 8 \div 2 = 4 \)
- \( 4 \div 2 = 2 \)
- \( 2 \div 2 = 1 \)
Counting the number of times we divided by 2, we find that 128 is divided by 2 a total of 7 times.
Thus, the prime factorization of 128 is:
\[ 128 = 2^7 \]
So, the answer is \( 2^7 \).