Answer
$\dfrac{4x^{7}}{9y^{10}}$
Work Step by Step
Use the laws of exponents to simplify the given expression, $
(3x^{-2}y^3)^{-2}(4x^3y^{-4})
.$
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}
(3^{-2}x^{-2(-2)}y^{3(-2)})(4x^3y^{-4})
\\\\=
(3^{-2}x^{4}y^{-6})(4x^3y^{-4})
.\end{array}
Using the law of exponents which states that $a^x\cdot a^y=a^{x+y},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
(3)^{-2}(4)x^{4+3}y^{-6+(-4)}
\\\\=
(3)^{-2}(4)x^{7}y^{-10}
.\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{(4)x^{7}}{(3)^{2}y^{10}}
\\\\=
\dfrac{4x^{7}}{9y^{10}}
.\end{array}
