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