#### Answer

$k^4p^{7}\sqrt[]{23k}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[]{23k^9p^{14}}
,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers.
$\bf{\text{Solution Details:}}$
Expressing the radicand of the expression above with a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[]{k^8p^{14}\cdot23k}
\\\\=
\sqrt[]{(k^4p^{7})^2\cdot23k}
\\\\=
k^4p^{7}\sqrt[]{23k}
.\end{array}