10＾500 read as ten to the power of five hundred?

I don't think that's wrong, but I would say 'ten to the five hundred.'

Thanks.
Without "power", would people misunderstand you?

I'm quite sure of it. The context makes it clear that the topic is related to math and science, so anyone who is reasonably science literate would be familiar with that sort of expression. Some might say 'ten to the five hundredth,' too. But the expression in the OP is fine, too.