Express each of the following as product of powers of their prime factors:
(i) 648             (ii) 405            (iii) 540          (iv) 3,600

Explanation

To express each of the given numbers as a product of powers of their prime factors, we will follow a systematic approach of dividing the numbers by prime factors until we reach 1. Let's solve each part step by step.

### (i) Expressing 648 as a product of powers of its prime factors:

1. Start with 648.
2. Divide by 2 (the smallest prime number):
- 648 ÷ 2 = 324
3. Divide 324 by 2:
...