Answer
$\color{blue}{-\dfrac{2}{x^4}}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
(4) $(ab)^m = a^mb^m$
(5) $(a^m)^n=a^{mn}$
(6) $a^m \cdot a^n = a^{m+n}$
(7) $a^0=1, a\ne0$
Use rule (6) above to obtain:
$=\dfrac{-8xy^{1+3}}{4x^5y^4}
\\=\dfrac{-8xy^4}{4x^5y^4}$
Divide the coefficients by cancelling out the common factors to obtain:
$\require{cancel}
\\=\dfrac{-\cancel{8}^2xy^4}{\cancel{4}x^5y^4}
\\=\dfrac{-2xy^4}{x^5y^4}$
Use rule (2) above to obtain:
$=-2x^{1-5}y^{4-4}
\\=-2x^{-4}y^{0}$
Use rule (7) above to obtain:
$=-2x^{-4}(1)
\\=-2x^{-4}$
Use rule (1) above to obtain:
$=-2 \cdot \dfrac{1}{x^4}
\\=\dfrac{-2}{x^4}
\\=\color{blue}{-\dfrac{2}{x^4}}$
