Answer
$\dfrac{81}{n^{4}}$
Work Step by Step
Using the laws of exponents, the given expression, $
(3n^{-1})^{4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
3^4n^{-1(4)}
\\\\=
81n^{-4}
\\\\=
\dfrac{81}{n^{4}}
.\end{array}
For more complicated problems, it is helpful to remember that you can flip the location of numbers with negative exponents. In other words, you can move numbers with a negative exponent that are in the numerator to the denominator, and you can move numbers with a negative exponent in the denominator to the numerator.
