Simplify the following:
5^28/(5^32×5^4)
Combine powers. 5^28/(5^32×5^4) = 5^(28 - 4 - 32):
5^(28 - 4 - 32)
28 - 4 - 32 = 28 - (4 + 32):
5^(28 - (4 + 32))
4 + 32 = 36:
5^(28 - 36)
28 - 36 = -(36 - 28):
5^(-(36 - 28))
| 2 | 16
| 3 | 6
- | 2 | 8
| 0 | 8:
5^(-8)
5^8 = (5^4)^2 = ((5^2)^2)^2:
1/((5^2)^2)^2
5^2 = 25:
1/(25^2)^2
| 2 | 5
× | 2 | 5
1 | 2 | 5
5 | 0 | 0
6 | 2 | 5:
1/625^2
| | | 6 | 2 | 5
× | | | 6 | 2 | 5
| | 3 | 1 | 2 | 5
| 1 | 2 | 5 | 0 | 0
3 | 7 | 5 | 0 | 0 | 0
3 | 9 | 0 | 6 | 2 | 5:
Answer: 1/390625
