To write 128 as a product of its prime factors in index form, let's break down 128 into its prime factors:

Start with 128: $128 \div 2 = 64$ $64 \div 2 = 32$ $32 \div 2 = 16$ $16 \div 2 = 8$ $8 \div 2 = 4$ $4 \div 2 = 2$ $2 \div 2 = 1$

We divided by 2 seven times, and no other prime factors appear.

Thus, the prime factorization of 128 is $2^7$.

So, the answer in index form is: $128 = 2^7$

Would you like more details or have any questions about this process?

Here are some related questions:

1. How can I use prime factorization to simplify fractions?
2. What is the importance of prime factorization in number theory?
3. How do I express other numbers in index form?
4. What is the relationship between prime factorization and finding the greatest common divisor?
5. Can prime factorization be used in solving algebraic equations?

Tip: Prime factorization is a great tool for simplifying large numbers and solving problems related to divisibility and least common multiples (LCM).