hhh...If you have the problem of 700MB....you have to look for a solution near to yours...
In fact, you can remarque that all the cases a%10(9cases) can be resumed into just one....mod 4 is the solution...
just you have to take cases b==0 and a==0, each one alone, then b%=4;
after that If b==0, you must put b=4 because when you look at case a%10==8, 8^0 is different from 8^4
Then you make b=pow(a, b)%10 and finally cout<<b<<'\n';

"a and b both are not 0" This means that when a == 0 then b != 0; when b==0 then a != 0.
A test case where a==0 and b==0 is excluded.

Really easy.. You don't even Need to remember pattern of various digits such as for 3->3,9,7,1 and so on.
was pending for 6 months.. 1 night simple idea, got AC in two mins.

this is not good mentioning that both a and b not zero.............

@avid coder
add
a=a%10 ; //0<= a<=20