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