A number $x$ is 3 larger than its reciprocal.  What is the value of $\left(x-\frac{1}{x}\right)^4$?
I need to find the value of $\left(x-\frac{1}{x}\right)^4$, but I also know that $x$ is 3 larger than its reciprocal, which means that $x-\frac{1}{x}=3$. This makes the problem much easier, because I can just plug in 3 for $\left(x-\frac{1}{x}\right)$ and simplify. So I have $\left(3\right)^4$, which is just 81. 