Answer
$\color{blue}{p^{11/6}}$
Work Step by Step
RECALL:
(1) $a^m \cdot a^n = a^{m+n}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $a^{1/n} = \sqrt[n]{a}$
(4) When $n$ is odd, $\sqrt[n]{a^n}=a$
(5) $a^{m/n} = \left(\sqrt[n]{a}\right)^m$
(6) $(ab)^m=a^mb^m$
(7) $(a^m)^n=a^{mn}$
(8) $a^{-m}=\dfrac{1}{a^m}$
Use rule (1) above to obtain:
$=\dfrac{p^{1/5+7/10+1/3}}{(p^3)^{-1/5}}
\\=\dfrac{p^{6/30+21/30+10/30}}{(p^3)^{-1/5}}
\\=\dfrac{p^{37/30}}{(p^3)^{-1/5}}$
Use rule (7) above to obtain:
$\\=\dfrac{p^{37/30}}{p^{3\cdot (-1/5)}}
\\=\dfrac{p^{37/30}}{p^{-3/5}}$
Use rule (2) above to obtain:
$=p^{37/30-(-3/5)}
\\=p^{37/30+3/5}
\\=p^{37/30 + 18/30}
\\=p^{55/30}
\\=\color{blue}{p^{11/6}}$
