(2^9/2^8 * sixth root of 3)^4

You are getting closer.

2^9/2^8 = 2^1 or more commonly known as 2.

because 2^(9-8) = 2^1

sixth root of three can be written as 3^(1/6)

so.

[ 2*3^(1/6) ]^4

Apply the 4 to inside the bracket

2^4 * 3^[ (1/6)*4) ]

16 * 3^(4/6)

16 * 3^(2/3)

=33.281341