I notice that the units digit of powers of 9 depends on the exponent. For example, $9^1$ has a units digit of 9, $9^2$ has a units digit of 1, $9^3$ has a units digit of 9 again, and so on. So the units digit of $9^k$ is either 9 or 1, depending on whether k is odd or even. Therefore, I need to find out if the exponent $8^7$ is odd or even. I recall that any power of an even number is even, so $8^7$ must be even. That means the units digit of $9^{8^7}$ is the same as the units digit of $9^2$, which is 1. 
Find the units digit of $9^{8^7}$.