\(AM radio waves<FM radio waves<Gamma rays<Micro waves\)
Step 1: Gamma rays have the shortest wavelengths in the electromagnetic spectrum.
Step 2: Microwaves have longer wavelengths than gamma rays but shorter than radio waves.
Step 3: Within radio waves, FM waves have shorter wavelengths compared to AM waves.
Step 4: Thus, the correct order from shortest to longest wavelength is gamma rays, microwaves, FM radio waves, and AM radio waves.