for these type of q we need to know the repetition
7^1=7 when div by 100 rem=7
7^2=49 rem=49
7^3=343 rem=43
7^4=2401 rem=1
7^5=16807 rem=7

hence the rem is repeating after every 4th power

7^10 (div 10 by 4 rem is 2 ; so 7^10 is a no. which will have same rem as 7^2 i.e 49)

ans is 49

I was basically trying to multiply them !! like this

7^10 = 49^5
=2401 * 2401 * 49

then it got harder ,, but I thought "if I multiply anything in 100 , it will not have a remainder when its divided by 100 !!"

so I skipped both the 2400 .. and it became like this :-
1 * 1 * 49 = 49 that's your answer