Surds and fractional indicies

I'm starting with basic simplification and while I thought I understood the rules I cannot seem to get the same answers as the book I am learning from.

The two questions that are vexing me are as follows:

Simplify:

1. $\displaystyle (3^3)^(1/2) * 9^(1/4)$

2. $\displaystyle CubeRoot(a^4b^5) * (b^(1/3))/a $

The answer for the first is 3^2 but I get 27^(7/4).

The second really makes me doubt by understanding as I swapped the first part around to read:

a^(4/3)b^(5/3) yet the book states this should be a^(3/4)b^(5/3).

Can anyone see where I am going wrong?