Answer
$-\dfrac{1875p^{13}}{8}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{\left(5p^3\right)^4\left(-3p^7\right)}{2p^2\left(4p^4\right)}
$, is equivalent to
\begin{align*}
&
\dfrac{\left(5^{1(4)}p^{3(4)}\right)\left(-3p^7\right)}{2p^2\left(4p^4\right)}
&(\text{use }\left(a^m\right)^n=a^{mn})
\\\\&=
\dfrac{\left(5^{4}p^{12}\right)\left(-3p^7\right)}{2p^2\left(4p^4\right)}
\\\\&=
\dfrac{\left(5^{4}\cdot(-3)\right)\left(p^{12}\cdot p^7\right)}{\left(2\cdot4\right)\left(p^2\cdot p^4\right)}
\\\\&=
\dfrac{-1875p^{12+7}}{8p^{2+4}}
&(\text{use }a^m\cdot a^n=a^{m+n})
\\\\&=
\dfrac{-1875p^{19}}{8p^{6}}
\\\\&=
-\dfrac{1875}{8}p^{19-6}
&(\text{use }\dfrac{a^m}{a^n}=a^{m-n})
\\\\&=
-\dfrac{1875p^{13}}{8}
.\end{align*}
Hence, the expression $
\dfrac{\left(5p^3\right)^4\left(-3p^7\right)}{2p^2\left(4p^4\right)}
$ simplifies to $
-\dfrac{1875p^{13}}{8}
$.
