Simplify $\left(\frac{100}{101}\right)^{-3}\left(\frac{100}{101}\right)^{3}$.
I notice that the bases of both powers are the same, so I can use the rule that $\left(\frac{100}{101}\right)^{-3}\left(\frac{100}{101}\right)^{3} = \left(\frac{100}{101}\right)^{-3 + 3}$. This simplifies to $\left(\frac{100}{101}\right)^{0}$. I recall that any nonzero number raised to the zero power is equal to 1, so the final answer is 1. 