Answer
$z^{-1/2} \left( 9+2z^{} \right)$
Work Step by Step
Factoring the given factor, $
z^{-1/2}
,$ then the given expression, $
9z^{-1/2}+2z^{1/2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
z^{-1/2} \left( \dfrac{9z^{-1/2}}{z^{-1/2}}+\dfrac{2z^{1/2}}{z^{-1/2}} \right)
\\\\=
z^{-1/2} \left( 9z^{-\frac{1}{2}-\left(-\frac{1}{2}\right)}+2z^{\frac{1}{2}-\left(-\frac{1}{2}\right)} \right)
\\\\=
z^{-1/2} \left( 9z^{-\frac{1}{2}+\frac{1}{2}}+2z^{\frac{1}{2}+\frac{1}{2}} \right)
\\\\=
z^{-1/2} \left( 9z^{0}+2z^{1} \right)
\\\\=
z^{-1/2} \left( 9(1)+2z^{} \right)
\\\\=
z^{-1/2} \left( 9+2z^{} \right)
.\end{array}
