Evaluating Fraction/exponent...

This is really driving me nuts, I've spent about 2 hours on and off trying to get to the given answer...With no close results.

Apologies for lack of formatted maths symbols.

(8/27)^3/2

The answer is given as (16/243)√6

I follow the normal process, as in: = √(8/27)^3

then go down the ((√2.√4)/(√3.√9))^3

= ((2√2)/(3√3))^3

This takes me nowhere near to (16/243)√6

If somone has the time, could you please show me how I can get to the (16/243)√6 and maybe explain the error of my process too.

It would be much appreciated

Thank you