Answer
$-\dfrac{2}{x^4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{(-8xy)y^3}{4x^5y^4}
.$
$\bf{\text{Solution Details:}}$
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-8xy^{1+3}}{4x^5y^4}
\\\\=
\dfrac{-8xy^{4}}{4x^5y^4}
\\\\=
\dfrac{\cancel4(-2)x\cancel{y^{4}}}{\cancel4x^5\cancel{y^{4}}}
\\\\=
\dfrac{-2x}{x^5}
.\end{array}
Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
-2x^{1-5}
\\\\=
-2x^{-4}
.\end{array}
Using the Negative Exponent Rule of the laws of exponents which states that $x^{-m}=\dfrac{1}{x^m}$ or $\dfrac{1}{x^{-m}}=x^m,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{-2}{x^4}
\\\\=
-\dfrac{2}{x^4}
.\end{array}
