how do you work out (4/9)^1.5? i know the answers 8/27 but not why?

Why don't you join up?  You are asking some good questions today :)

$$\\\left(\frac{4}{9}\right)^{1.5}\\\\
=\left(\frac{4}{9}\right)^{3/2}\\\\
=\left(\left(\frac{4}{9}\right)^{1/2}\right)^3\\\\
=\left(\frac{\sqrt4}{\sqrt9}\right)^3\\\\
=\left(\frac{2}{3}\right)^3\\\\
=\frac{2^3}{3^3}\\\\
=\frac{8}{27}\\\\$$

Remember that 1.5 = 3/2.....so we have

(4/9)^3/2  = [(4/9)^1/2]³ =  [√(4/9)]³   = (2/3)³ = 8/27