Answer
$p+2p^{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the Distributive Property and the laws of exponents to simplify the given expression, $
p^{2/3} \left( p^{1/3}+2p^{4/3} \right)
.$
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
p^{2/3}(p^{1/3})+p^{2/3}(2p^{4/3})
.\end{array}
Using the Product Rule of the laws of exponents which is given by $x^m\cdot x^n=x^{m+n},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
p^{\frac{2}{3}+\frac{1}{3}}+2p^{\frac{2}{3}+\frac{4}{3}}
\\\\=
p^{\frac{3}{3}}+2p^{\frac{6}{3}}
\\\\=
p^{1}+2p^{2}
\\\\=
p+2p^{2}
.\end{array}