How old is a rock with a half life of 5,280 years
if 1/8th of the parent material is left?

A rock with a half-life of 5,280 years having 1/8th of the parent material left will be 15,840 years old.

Explanation:

The half-life of a material is the time needed for only half of the parent material to be left, while half has is gone, or rather has disintegrated. The half-life is used further into the falling apart of the parent material though, with the same principle being applied. Practically, from the 1/2 of the parent material being left, the half-life of it would mean 1/4 of the parent material being left, and from that 1/4, the half-life would be at 1/8 of the parent material being left, and so one, by simply dividing in two.

In this case, having a half-life of the rock of 5,280 years, we will simply need to add that amount of years on every next phase. So, the half-life is 5,280 when 1/ of the parent material is left. When 1/4 of the parent material will be left we will have an age of 10,560 years, while when only 1/8 is left, we will have 15,840 years of age for the rock.