How do we know God is all-powerful?

I know God exists. I know God is good because I've experienced things that are evil, but not from God. I know God is all-knowing because if you're faithful, He will give you a way out. But, how do we know God is all-powerful? If He is, then He will have to explain the problem of evil and every evil action done, every trial as to why it was according to His purpose.