#### Answer

no solution

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given radical equation, $
\sqrt[4]{8z-3}+2=0
,$ use the properties of equality to isolate the radical expression. Then ensure that the right side of the equal sign is positive.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the radical expression results to
\begin{array}{l}\require{cancel}
\sqrt[4]{8z-3}=-2
.\end{array}
The left side of the equal sign always gives a non negative result. This will never be equal to the negative value at the right side. Hence, there is $\text{
no solution
.}$