To express 675 as a product of its prime factors in index form, we begin by performing a prime factorization.

1. Divide 675 by 3 (the smallest prime factor): $675 \div 3 = 225$

2. Now, divide 225 by 3 again: $225 \div 3 = 75$

3. Then, divide 75 by 3 again: $75 \div 3 = 25$

4. Next, divide 25 by 5 (the next prime factor): $25 \div 5 = 5$

5. Finally, divide 5 by 5: $5 \div 5 = 1$

So, the prime factorization of 675 is: $675 = 3^3 \times 5^2$

Therefore, the prime factorization of 675 in index form is $3^3 \times 5^2$.

Would you like more details or further explanation?

Here are some related questions you may find interesting:

1. How do you perform a prime factorization for larger numbers?
2. What is the significance of prime factorization in simplifying expressions?
3. Can you explain the difference between index form and expanded form?
4. How would the prime factorization of a number like 840 look?
5. How do you use prime factorization to find the greatest common divisor (GCD) of two numbers?

Tip: Remember that when dividing by a prime factor, you continue dividing the result by the same prime as long as it divides evenly, before moving to the next prime.