1. 3^302 mod 5 using Modulo

Solution:
`3^302" mod "5`

Here `3^302=(3^2)^151`

`=(3^2" mod "5)^151" mod "5`

`=(9" mod "5)^151" mod "5`

`=4^151" mod "5`

Here `4^151=(4^2)^75*4`

`=(((4^2" mod "5)^75" mod "5)*(4" mod "5))" mod "5`

`=(((16" mod "5)^75" mod "5)*4)" mod "5`

`=((1^75" mod "5)*4)" mod "5`

`=((1" mod "5)*4)" mod "5`

`=(1*4)" mod "5`

`=4" mod "5`

`=4`