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