Answer
$-\dfrac{3}{x^4}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{-24x^{-6}}{8x^{-2}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(-24\div8)x^{-6-(-2)}
\\\\=
-3x^{-6+2}
\\\\=
-3x^{-4}
\\\\=
-\dfrac{3}{x^4}
.\end{array}
For more complicated problems, it is helpful to remember that you can flip the location of numbers with negative exponents. In other words, you can move numbers with a negative exponent that are in the numerator to the denominator, and you can move numbers with a negative exponent in the denominator to the numerator.
