#### Answer

$4t\sqrt[3]{3st}-3s\sqrt{3st}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt[3]{192st^4}-\sqrt{27s^3t}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{64t^3\cdot3st}-\sqrt{9s^2\cdot 3st}
\\\\=
\sqrt[3]{(4t)^3\cdot3st}-\sqrt{(3s)^2\cdot 3st}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
4t\sqrt[3]{3st}-3s\sqrt{3st}
.\end{array}