Could you rephrase your question? I am a bit confused by the current phrasing.
Do you mean, "to change 16^8 to a base 4"
Or "to change 16^8 to a base with the digit 4"?
Or do you mean something else entirely?
16 = 4^2
So we have
(4^2)^8 = 4^32 = a really big number....!!!.....18,446,744,073,709,551,616
> 18 quintillion
I am going to interprete this differently Chris. [ Plus 2*8=16 LOL ]
we count in base 10 so we use 10 digits that is 0,1,2,3,4,5,6,7,8,9 the next on is 10 etc
if we were counting in base 4 the numbers would be 0,1,2,3,10,11,12,13,20,21,22,23,30,31,32,33,100, etc
$$\\16^8=(4^2)^8=4^{16}\\\\$$
If we write this base 10 number as a base 4 number then the answer is
10,000,000,000,000,000 that is a 1 followed by 16 zeros - base 4