Thank you for the opportunity to help you with your question! Hope your day is going well!
The reason why we must stipulate that b does not equal 0, is the fact that it would make the equation invalid (since you can never divide by zero). Otherwise, it does not matter for the simplification.
This is a laws of exponents problem. Technically a is raised to the 1 power, and b is raised to the 1 power. Since it is a power raised to another power, you multiply.
Or you can use the identity
Either way is a great way to think about it.
Please let me know if you need any clarification. I'm always happy to answer your questions.