Answer
$\dfrac{16}{x^{6}y^{16}}$
Work Step by Step
Use the laws of exponents to simplify the given expression, $
(-2x^4y^{-3})^0(-4x^{-3}y^{-8})^2
.$
Using the law of exponents which states that $a^0=1,$ the expression above simplifies to
\begin{array}{l}\require{cancel}
(1)(-4x^{-3}y^{-8})^2
\\\\=
(-4x^{-3}y^{-8})^2
.\end{array}
Using the law of exponents which states that $(a^xb^y)^z=a^{xz}b^{yz},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
(-4)^2x^{-3(2)}y^{-8(2)}
\\\\=
16x^{-6}y^{-16}
.\end{array}
Using the law of exponents which states that $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{16}{x^{6}y^{16}}
.\end{array}
