The half-life of a radioactive substance is the time it takes for half of the substance to decay. The remaining fraction of the original substance after a certain number of half-lives can be calculated using the formula: N=N0(‌
1
2
)‌
t
T1∕2
Where: N is the remaining quantity of the substance, N0 is the initial quantity of the substance, t is the elapsed time, T1∕2 is the half-life of the substance. Given that the half-life T1∕2 is 1600 years, and we want to find the amount of substance left after 6400 years, we can use the above formula: ‌
t
T1∕2
=‌
6400
1600
=4‌ half-lives ‌ Therefore, ‌N=N0(‌
1
2
)4 ‌N=N0(‌
1
24
) ‌N=N0(‌
1
16
) The fraction of the original sample remaining undecayed after 6400 years is ‌