Answer
$\dfrac{1}{16n^6}$
Work Step by Step
Using the laws of exponents, the given expression, $
(4n^{3})^{-2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
4^{-2}n^{3(-2)}
\\\\=
4^{-2}n^{-6}
\\\\=
\dfrac{1}{4^2n^6}
\\\\=
\dfrac{1}{16n^6}
.\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.
