(I don't think that anyone should use "exponentially" that way: it is an art term with a specific and particular meaning, so find another word if you mean something else! Like misusing specific legal or sporting terms...)
"to O(xxx)" is a good idea, in terms of keeping it mathematical and accurate. I like that best. "hugely" makes me giggle, because I really hear "bigly" when I see/hear it.
If you have that tendency, you just need to think of TAOCP, this industry's best distillation of intellectual achievement, with the word "art" in its name.
(I don't think that anyone should use "exponentially" that way: it is an art term with a specific and particular meaning, so find another word if you mean something else! Like misusing specific legal or sporting terms...)