Answer
The fraction of plutonium that is left is $~~1.2\times 10^{-17}$
Work Step by Step
When half of a sample of $^{238}U$ has decayed, the time that has passed is $4.5\times 10^9~y$
We can express this time period as the number of half-lives of plutonium:
$\frac{4.5\times 10^9~y}{8.0\times 10^7~y} = 56.25$
We can find the fraction of plutonium that is left:
$(\frac{1}{2})^{56.25} = 1.2\times 10^{-17}$
The fraction of plutonium that is left is $~~1.2\times 10^{-17}$
