#### Answer

$3z^{5/4}+5z^{2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the laws of exponents to simplify the given expression, $
z^{5/8} \left( 3z^{5/8}+5z^{11/8} \right)
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
z^{5/8}( 3z^{5/8})+z^{5/8}(5z^{11/8})
.\end{array}
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3z^{\frac{5}{8}+{\frac{5}{8}}}+5z^{\frac{5}{8}+\frac{11}{8}}
\\\\=
3z^{\frac{10}{8}}+5z^{\frac{16}{8}}
\\\\=
3z^{\frac{5}{4}}+5z^{2}
\\\\=
3z^{5/4}+5z^{2}
.\end{array}