In Agile, there is no rule on the ratio of the product owner and the scrum teams. A product owner is aligned with a single product and this person takes care of keeping it healthy. It might be a possibility that multiple teams are aligned to deliver that product, in this case, it will be overwhelming for the product owner to TAKE care of all the teams, answering their queries, sitting in their planning meetings, etc. 

In real-life scenarios, we try to align maximum of 3 – 4 teams per product owner, if it exceeds the number, one can have proxy product owners who can INDIRECTLY help the main product owner to manage the product and teams. With proxy product owners, there will be a NEED for coordination and alignment. All the proxy owner will need to stay in sync with the main product owner so as to achieve the desired results. Though it is encouraged to have a single Product BACKLOG and a single PO being responsible for return-on-investment when developing one product. Having a single Product Owner creates transparency and enables PROPER empiricism. It also depends on the size of the product, if it is too large, it should be broken down further to create sub-products and those should be aligned with different product owners.