#### Answer

$z=16$

#### Work Step by Step

Using the properties of equality, the given equation, $
z^{1/4}+8=10
$, is equivalent to
\begin{array}{l}
z^{1/4}=10-8
\\\\
z^{1/4}=2
.\end{array}
Raising both sides to the $\text{
4th
}$ power, the solution to the equation above, $
z^{1/4}=2
$, is
\begin{array}{l}
z=(2)^4
\\\\
z=16
.\end{array}
Upon checking, $
z=16
$ satisfies the given equation.