Mathematics

Problem

Let

P = \dfrac{(\sqrt[5]{243})^{3/2}}{\sqrt{\sqrt[3]{27}}}

. a. (i) Express every radical and power in

P

using rational exponents only. b. (ii) Simplify the numerator and the denominator separately, writing each as a power of

3

. c. (iii) Hence simplify

P

completely and state its value as an integer.