Answer
$q^{-3} \left( -5+8q \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Factor the variable with the lesser exponent in the given expression, $
-5q^{-3}+8q^{-2}
.$ Then, divide the given expression and the variable with the lesser exponent.
$\bf{\text{Solution Details:}}$
Factoring $
q^{-3}
$ (the variable with the lesser exponent), the expression above is equivalent to
\begin{array}{l}\require{cancel}
q^{-3} \left( \dfrac{-5q^{-3}}{q^{-3}}+\dfrac{8q^{-2}}{q^{-3}} \right)
.\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}
q^{-3} \left( -5q^{-3-(-3)}+8q^{-2-(-3)} \right)
\\\\=
q^{-3} \left( -5q^{-3+3}+8q^{-2+3} \right)
\\\\=
q^{-3} \left( -5q^{0}+8q^{1} \right)
\\\\=
q^{-3} \left( -5(1)+8q \right)
\\\\=
q^{-3} \left( -5+8q \right)
.\end{array}