Answer
$48x^{2a}$
Work Step by Step
Using the laws of exponents, the given expression, $
3x^{4a} \left( 4x^{-a} \right)^2
,$ simplifies to
\begin{array}{l}\require{cancel}
3x^{4a} \left( 4^2x^{-a(2)} \right)
\\\\=
3x^{4a} \left( 16x^{-2a} \right)
\\\\=
48x^{4a+(-2a)}
\\\\=
48x^{2a}
.\end{array}
