Yes, in a vacuum, all electromagnetic waves would travel at the same speed, which is the speed of light in a vacuum, denoted by 'c'. According to the theory of special relativity, the speed of light is a fundamental constant of nature and is approximately 299,792,458 meters per second (or about 186,282 miles per second).
This principle is often summarized by the statement that "in a vacuum, the speed of light is constant and independent of the observer's motion." It means that whether it's visible light, radio waves, microwaves, X-rays, or any other part of the electromagnetic spectrum, they would all propagate at the same speed in the absence of any medium.
It's worth noting that when electromagnetic waves pass through a medium like air, water, or glass, their speed may be slightly reduced due to interactions with the atoms or molecules in that medium. This reduction in speed is responsible for phenomena such as refraction. However, in a vacuum where there is no medium, all electromagnetic waves would travel at the same speed, c.