There are a few different issues at work here. First is the concept of variable maximum aperture, which some zooms have, and some don't. Then there's the fact that when changing focal lengths, or zooming, the aperture will change in one of two ways; either the actual opening changes size, to match a given f-stop with the changing focal length, or the opening doesn't change, and you get a different effective f-stop from the same opening, based on the FL you are zoomed to. With auto-exposure of any kind, the camera should compensate to provide correct exposure. With manual gear, you may or may not need to re-meter after you have zoomed, depending upon the design of the lens. Most lenses these days will stop down to the indicated f-stop, regardless of focal length selected.
With variable maximum aperture lenses, as you zoom to longer lengths, the wide open aperture remains physically the same size, but becomes a relatively smaller opening and f-stop. For instance, a 24-85 f3.5-5.6 zoom gives f3.5 wide open at 24mm FL; when you zoom to 85mm, without touching the aperture ring, the same wide-open setting now gives f5.6. If you set this lens to 50mm, the wide open aperture is probably around f4. Since aperture is relative to focal length, as you change length and leave the physical size of the opening the same, the effective aperture changes.
Now, if you are using manual flash and working wide open with a variable aperture zoom, you may have some trouble. But if you set this same lens to, say, f8, if should be the same f8 at all focal lengths- that is, different physical size, giving f8 at that length. The mechanism in the lens will adjust to the correct opening to give f8 at the selected focal length. Manual flash exposure becomes easy.
Constant mazimum aperture zooms are really nice, since you don't lose any speed as you zoom, but they are very expensive, and larger and heavier. By and large, these are one of the major differences between most "professional" zooms and many "consumer" zooms. The good news is that (except for camera/lens combinations that only offer stop-down metering) any TTL meter- on auto settings or manual setting- will give correct exposure when using zooms, regardless of how they are set. So don't worry.