I have D5000 Nikon and am looking for a longer zoom to take pictures of wildlife (live in Montana Rockies). I also have a Canon Powershot with 40x zoom - and the lens I have for my Nikon has a comparable zoom as the 40x. What lens should I get for my Nikon so I have 60x to 80x zoom?
The rule is learn to get closer. Really the best wildlife shots are made by people who have learned to get closer to wildlife ( a tricky skill ) and to wait ( find a spot you think they'll come near and wait there, usually partly hidden ). These are like hunter's skills.
Also note that 40x is a factor from widest focal length on a zoom to longest. It's not a focal length. I don't know of any 40x zoom for F-mount ( that would be like an 18-720 mm ). It's worth noting that Nikon's longest F-mount focal length is 800mm and it costs an alarming $16,000.
So you need to learn to get closer.
For wildlife photography, the general rule is that too much focal length is never enough. Instead of a zoom lens that you'll use maxxed out most of the time, get a telephoto prime lens. You'll get a more optimized lens for your use case than a zoom.
You might also get a teleconverter for more focal length at the expense of light gathering capability, and probably some in image quality.
Zoom is not equal to the area which the object occupies on the final image, "40x" or "80x" represent the ratio between how small and how big same object can be rendered on the frame and technically say nothing about camera being suitable for wildlife.
Generally speaking there are no affordable equivalent objectives for your Nikon D5000 i.e. those which will give you the same object size as a Canon Powershot with 40x zoom. This happens because technical reasons prevent creation of lightweight, cheap enough and long (magnificating) enough objective for all popular DSLRs.
You can get good reach (almost the same as with you Canon camera but still worse) at a good enough price with a Sigma 150-500mm or Sigma 120-400mm but this is a heavy and expensive compared to D5000 and you would still need second objective for non-wildlife scenery.
If you want a compromise between lightweightness and quality you should better look at Micro4/3 cameras.
First, as others have said, zoom factor is just the amount of focal length change from the widest focal length to the longest focal length. It does not really relate to an actual focal length of a lens.
Second, the Powershot's long focal length is an effective 960mm. They get that number in part from the crop factor of the really small image sensor. That is a whole different and long discussion.
Typically nature photographers will want focal lengths between 400 and 800mm lenses at the longest focal length. Some will go with primes and some will go with zoom lenses. However, even at the widest the quality long focal lengths will be no wider than between like 150mm and 300mm.
The most important thing to remember is that the wider the range of focal lengths the less quality you will get in a lens. It is impossible to make a high quality lens that would cover say 24 to 800mm focal length. You have to make so many compromises to make zoom lenses, and the wider the range the more the compromises. When you look at DSLR lenses the superzoom (wide range) go from like 18 to 200mm or there abouts. You won't find any superzoom that will top out much more than 240 to 300mm. The reason a DSLR has interchangeable lenses is so you can have quality glass.
You will also find that quality extremely long focal length lenses are very expensive. If you are only shooting nature a couple times a year then it is much more affordable to rent a lens. You can rent something like a 200-500mm for around $80 for 7 days where it would be like $1,500 or more to buy it. And some lenses that are in the price range of $6,000 to buy are like $200 for a week.
If you want to purchase a lower end long focal length lens you could look at the Tamron 150-600mm f/5-6.3 for around $900-1,000. It is a quality lens for the price and includes stabilization. It would work well on your D5000 and give an effective long end of 900mm (about the same as the long end of your PowerShot).
What lens should I get for my Nikon so I have 60x to 80x zoom?
Such lens doesn't exist for F mount (or any other DSLR mount for that matter) to my knowledge.
As for zoom ratio, it's just an expression reflecting the ratio between the shortest and the longest focal length of a lens. I don't know exactly what Canon PowerShot you own, but let's take the latest 40× zoom I could find - the PowerShot SX720 HS. It has a 24-960 mm equivalent lens. 960/24 equals exactly 40, so there you have it. "Equivalent" means that if you mount a hypothetical 24-960 mm lens on a full frame camera, you will have the same field of view.
The larger the sensor is, the harder it is to create a lens with a large zoom ratio. The biggest ratio zoom for crop sensor (DX) Nikon I can think of is a Nikon 18-300 and a Sigma with the same focal length. That's roughly а 16.66× zoom which may seem not at all impressive compared to compact cameras.
Zoom ratio aside, if you're just looking to get similarly close as with your compact, look at the Nikon 200-500 f/5.6 or the Sigma/Tamron 150-600 f/5 - 6.3. Since the D5000 has a 1.5× crop factor, these are 750 and 900 mm equivalents at their long end. If you're on a tighter budget, a Nikon 70-300 (or a similar Sigma/Tamron) might still do a decent job.
What you should look at for this purpose is the effective focal length. A 40x zoom means the ratio between the maximum and minimum is 40, but that doesn't say what the maximum is. Usually the minimum is 24 or 25, which would imply that the maximum is 960 or 1000, but it could be that the minimum is 20 and the maximum is 800. In any case you already have at least as long a lens as Nikon offers for a DSLR. You are making compromises because of the small sensor. The Nikon P900 advertises an 83x zoom but I couldn't get specs on focal length from the Nikon site. The Canon SX60 reaches to 1365mm, so that would meet what you are asking for. This is certainly not a substitute for getting closer, but sometimes that is not an option.