# What fraction of the amount of carbon-14 that was the mammoth's tooth when it died is left after five half-lives?

Well, after 5 half-lives, should it not be....${\left(\frac{1}{2}\right)}^{5}$?
Which is what? ${\left(\frac{1}{2}\right)}^{5} = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{32}$
And so there is a $\frac{1}{32}$ fraction of the original ""^14C in the sample....