Answer
$P\left( \dfrac{2}{3} \right)=\dfrac{968}{243}$
Work Step by Step
Substituting $x$ with $
\dfrac{2}{3}
$ in $
P(x)=x^5-2x^3+4x^2-5x+6
$, then
\begin{array}{l}
P\left( \dfrac{2}{3} \right)=\left( \dfrac{2}{3} \right)^5-2\left( \dfrac{2}{3} \right)^3+4\left( \dfrac{2}{3} \right)^2-5\left( \dfrac{2}{3} \right)+6
\\\\
P\left( \dfrac{2}{3} \right)=\dfrac{32}{243}-2\left( \dfrac{8}{27} \right)+4\left( \dfrac{4}{9} \right)-5\left( \dfrac{2}{3} \right)+6
\\\\
P\left( \dfrac{2}{3} \right)=\dfrac{32}{243}-\dfrac{16}{27}+\dfrac{16}{9}-\dfrac{10}{3}+6
\\\\
P\left( \dfrac{2}{3} \right)=\dfrac{968}{243}
.\end{array}