Why does 0^0 = 1?

I really enjoy the Better Explained blog. Today at lunch I mentioned one entry Understanding Exponents (Why does 0^0 = 1?) that starts like this:

We’re taught that exponents are repeated multiplication. This is a good introduction, but it breaks down on 3^1.5 and the brain-twisting 0^0. How do you repeat zero zero times and get 1 — without melting your brain?

You can’t, not while exponents are repeated multiplication. Today our mental model is due for an upgrade.

I really enjoy the way the Better Explained blog tries to:

share hard-won “a ha!” moments in clear and simple language

The question was raised at lunch: "Is the Better Explained blog interesting to someone who does not have a math background?"

What do you think?

--Tom