(a) Write

\(\frac{x(27xy^3)^{\frac53}}{\sqrt[4]{81y^5}}\)

in the form \(3^a x^b y^c\), where \(a\), \(b\) and \(c\) are constants.

(b)

(i) Find the value of \(a\) such that

\(2\log_a8=\frac32.\)

(ii) Write \(\log_{a^2}3a\) as a single logarithm to base \(a\).