Mathematics

Problem

Let

E = \dfrac{\sqrt[3]{216p^{7}q^{5}}}{\sqrt{24p^{2}q}}

, where

p,q>0

. a. (i) Simplify the numerator

\sqrt[3]{216p^{7}q^{5}}

. b. (ii) Simplify the denominator

\sqrt{24p^{2}q}

. c. (iii) Hence, express

E

in its simplest radical form.