Answer
$1$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $
\dfrac{x^2-6x-16}{2x^2-128}\div\dfrac{x^2+10x+16}{x^2+16x+64}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^2-6x-16}{2x^2-128}\cdot\dfrac{x^2+16x+64}{x^2+10x+16}
\\\\=
\dfrac{(x-8)(x+2)}{2(x^2-64)}\cdot\dfrac{(x+8)(x+8)}{(x+8)(x+2)}
\\\\=
\dfrac{(\cancel{x-8})(\cancel{x+2})}{2(\cancel{x+8})(\cancel{x-8})}\cdot\dfrac{(\cancel{x+8})(\cancel{x+8})}{(\cancel{x+8})(\cancel{x+2})}
\\\\=
1
.\end{array}
