when a number is raised to the power of a rational number it becomes a root of the denominator's order and the number inside the root is raised by the power of the numerator
for example
[tex]x^{\frac{a}{b} }=\sqrt[b]{x^a}[/tex]
in this case
[tex]32^{\frac{3}{5} }=\sqrt[5]{32^3}[/tex]
[tex]=\sqrt[5]{32768}[/tex]
=8
