Answer
$\dfrac{1}{2pq}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{(3pq)q^2}{6p^2q^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{3pq^{1+2}}{6p^2q^4}
\\\\=
\dfrac{\cancel3pq^{3}}{\cancel3(2)p^2q^4}
\\\\=
\dfrac{pq^{3}}{2p^2q^4}
.\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}
\dfrac{p^{1-2}q^{3-4}}{2}
\\\\=
\dfrac{p^{-1}q^{-1}}{2}
.\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{1}{2p^{1}q^{1}}
\\\\=
\dfrac{1}{2pq}
.\end{array}
