Answer
$\dfrac{3x^5}{25y^4}$
Work Step by Step
Using laws of exponents, the given expression simplifies to
\begin{align*}
&
\left( 5x^2y^4 \right)^{-2}(3x^9y^4)
\\\\&=
\left( 5^{-2}x^{2(-2)}y^{4(-2)} \right)(3x^9y^4)
\\\\&=
\dfrac{1}{5^2}\left( x^{-4}y^{-8} \right)(3x^9y^4)
\\\\&=
\dfrac{3}{25}\left( x^{-4+9}y^{-8+4} \right)
\\\\&=
\dfrac{3}{25}\left( x^{5}y^{-4} \right)
\\\\&=
\dfrac{3x^5}{25y^4}
.\end{align*}
