Why do whole numbers raised to an exponent get greater while fractions raised to an exponent get smaller?

A whole number is a group of whole things. When you take a group of
whole things several times, you wind up with more things.

A [proper] fraction is a piece of a whole thing. When you take a piece of
the piece, you wind up with less of the whole thing.

(By the way ... your question and this whole answer are only true
when the exponent is greater than 1, and I haven't completely
figured out the rule for negative exponents yet.)