1. Find 5th root of 100000

Solution:
First find factors of 100000

2	100000
2	50000
2	25000
2	12500
2	6250
5	3125
5	625
5	125
5	25
5	5
	1

`100000=2 xx 2 xx 2 xx 2 xx 2 xx 5 xx 5 xx 5 xx 5 xx 5`

`100000=2^5 * 5^5`

Taking 5th root
`:. root (5)(100000)=root (5)(2^5 * 5^5)`

`=2 × 5`

`=10`

`:.` 100000 is a perfect `5^(th)` power