0|
Number |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Power of 1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
Power of 2 |
0 |
1 |
4 |
9 |
6 |
5 |
6 |
9 |
4 |
1 |
|
Power of 3 |
0 |
1 |
8 |
7 |
4 |
5 |
6 |
3 |
2 |
9 |
|
Power of 4 |
0 |
1 |
6 |
1 |
6 |
5 |
6 |
1 |
6 |
1 |
|
Power of 5 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Cyclicity of 0, 1, 5, 6 – 1 time
Cyclicity of 4, 9 – 2 times
Cyclicity of 2, 3, 7, 8 – 4 times
What is the unit digit of (217)^413×(819)^547×(414)^624×(342)^812 ?
- Power series of 7 i.e units digit 7 power expansion has 7,9,3 and 1 and it is raised to power 413 i.e 413/4 remainder 1 and so last digit is 7.
- Power series of 9 i.e units digit 9 power expansion has 9 and 1 and it is raised to power 547 i.e 547/2 remainder 1 and so last digit is 9.
- Power series of 4 i.e units digit 4 power expansion has 4 and 6 and it is raised to power 624 i.e 624/2 remainder 0 and so last digit is 6
- Power series of 2 i.e units digit 2 power expansion has 2,4,8 and 6 and it is raised to power 812 i.e 812/4 remainder 0 and so last digit is 6.
- All the last digits product=7*9*6*6 =8.
