Answer
$\dfrac{1}{a^{23}}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{a^{-6}(a^{-8})}{a^{-2}(a^{11})}
.$
$\bf{\text{Solution Details:}}$
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{a^{-6+(-8)}}{a^{-2+11}}
\\\\=
\dfrac{a^{-6-8}}{a^{-2+11}}
\\\\=
\dfrac{a^{-14}}{a^{9}}
.\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}
a^{-14-9}
\\\\=
a^{-23}
.\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}{a^{23}}
.\end{array}
