Answer
$2k^{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of exponents to simplify the given expression, $
\dfrac{12k^{-2}(k^{-3})^{-4}}{6k^5}
.$
$\bf{\text{Solution Details:}}$
Using the Power Rule of the laws of exponents which is given by $\left( x^m \right)^p=x^{mp},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{12k^{-2}k^{-3(-4)}}{6k^5}
\\\\=
\dfrac{\cancel6(2)k^{-2}k^{12}}{\cancel6k^5}
\\\\=
\dfrac{2k^{-2}k^{12}}{k^5}
.\end{array}
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{2k^{-2+12}}{k^5}
\\\\=
\dfrac{2k^{10}}{k^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}
2k^{10-5}
\\\\=
2k^{5}
.\end{array}
