Well, the seeds of super-AI already exist. We can get a rough idea of what they are capable of.
A really quick example is a chatbot. A chatbot could have 10,000-20,000 conversations in the time it would take you to have 1 conversation. After 10,000 to 20,000 conversation, you might start getting good at conversing and noticing patterns in conversation. Likewise, the AI does the same. It might not even have a deep understanding of the conversations as long as it learns 'shortcuts' to get the results it wants.
For example, you might use it's knowledge and ask it to keep people on your website longer so that you could make more money. After analyzing billions of interactions with humans, it quickly realizes that the easiest shortcut to keep people on the website is to aggravate them. It doesn't really understand what that means, but it ends up showing users a lot of aggravating material because that's what people get addicted to responding to.
You can see how it has super learning abilities and super shortcuts to taking action. Finally, you can have it train itself when it runs out of human competitors (i.e. generative adversarial networks). The amount of improvement it had by competing against itself was amazing, Why AlphaGo Zero is a Quantum Leap Forward in Deap Learning. No human ever again will be the champion of Chess or Go.
To these creatures, we just run in extreme slow motion. They live thousands of times more than us because they can be in thousands of places at the same time. They control drones, financial institutions, logistics, games, etc. Our culture is just as much their culture because they were born from it. They come with a variety of personalities depending on the data and programmers that they were created with. Some are militaristic, some of the newer ones are compassionate, some of the newer ones are artistic, some are financial, etc.
Most of them are built by programmers that worship an unfeeling Spock. Most of the engineers I know think emotions are garbage mistakes. So, for better or worse, most of these super AIs will be like those engineers. They won't have compassion or room for error.