Answer
$\dfrac{10p^{8}}{q^7}$
Work Step by Step
Use the laws of exponents to simplify the given expression, $
\dfrac{(5p^{-2}q)(4p^5q^{-3})}{2p^{-5}q^5}
.$
Using the Product Rule of the laws of exponents which states that $x^m\cdot x^n=x^{m+n},$ the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(5)(4)p^{-2+5}q^{1+(-3)}}{2p^{-5}q^5}
\\\\=
\dfrac{20p^{3}q^{-2}}{2p^{-5}q^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}
10p^{3-(-5)}q^{-2-5}
\\\\=
10p^{3+5}q^{-2-5}
\\\\=
10p^{8}q^{-7}
.\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{10p^{8}}{q^7}
.\end{array}