All electromagnetic waves travel at the same speed in a vacuum. however, different kinds of electromagnetic waves have different wavelengths. for example, microwaves have longer wavelengths than visible light. how is it possible for Both microwaves and visible light to travel at the same speed in a vacuum if they have different wavelengths

The reason for qualifying 'in vacuum' is because EM waves of different frequencies often propagate at different speeds through material.

Explanation:

Electromagnetic waves include visible light, radio waves, X-rays, and so on. What distinguishes these different bands of light is their frequency (or wavelength). But what they all have in common is that they travel at the same speed in vacuum.

The reason for qualifying 'in vacuum' is because EM waves of different frequencies often propagate at different speeds through material.

The speed of a wave c, its wavelength λ and frequency f are all related according to c=λf. So if c is the same for all EM waves, then if you (say) double the frequency of a wave, its wavelength will halve.

the denominator has a very specific role.