Answer
$512a^{}b^{8}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(2a^{-1}b^2)^3}{(8a^2b)^{-2}}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2^{1(3)}a^{-1(3)}b^{2(3)}}{8^{1(-2)}a^{2(-2)}b^{1(-2)}}
\\\\=
\dfrac{2^{3}a^{-3}b^{6}}{8^{-2}a^{-4}b^{-2}}
\\\\=
2^{3}\cdot8^2a^{-3-(-4)}b^{6-(-2)}
\\\\=
8\cdot64a^{-3+4}b^{6+2}
\\\\=
512a^{1}b^{8}
\\\\=
512a^{}b^{8}
.\end{array}
