Answer
$\dfrac{1}{(p+q)^5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{(p+q)^4(p+q)^{-3}}{(p+q)^6}
.$
$\bf{\text{Solution Details:}}$
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{(p+q)^{4+(-3)}}{(p+q)^6}
\\\\=
\dfrac{(p+q)^{4-3}}{(p+q)^6}
\\\\=
\dfrac{(p+q)^{1}}{(p+q)^6}
.\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}
(p+q)^{1-6}
\\\\=
(p+q)^{-5}
.\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}{(p+q)^5}
.\end{array}
