Answer
$(5+3st)\sqrt[4]{s^3t}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\sqrt[4]{625s^3t}+\sqrt[4]{81s^7t^5}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
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[4]{625\cdot s^3t}+\sqrt[4]{81s^4t^4\cdot s^3t}
\\\\=
\sqrt[4]{(5)^4\cdot s^3t}+\sqrt[4]{(3st)^4\cdot s^3t}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
5\sqrt[4]{s^3t}+3st\sqrt[4]{s^3t}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(5+3st)\sqrt[4]{s^3t}
.\end{array}
