Fractions and powers)

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

$${\left({\frac{{\mathtt{4}}}{{\mathtt{9}}}}\right)}^{\left({\frac{{\mathtt{3}}}{{\mathtt{2}}}}\right)} = {\frac{{\mathtt{8}}}{{\mathtt{27}}}} = {\mathtt{0.296\: \!296\: \!296\: \!296\: \!296\: \!3}}$$

Easiest to first take the square root of the fractionsince they are both squares, then cube the result. For example the square root of 4 is 2 and 2 cubed is 8.