My friend and I are each trying to form the integers from $0$ to $100$ using the numbers $2, 3, 8, 9$. We are only allowed to use the five basic operations: addition, subtraction, multiplication, division, exponentiation, as well as parentheses. No concatenation is allowed. Each expression must use all four of $2,3,8,9$ exactly once.
After we work on the problem for a while, I find 89 different integers, while my friend only finds 88 different integers. We compare our work, and we realize that I found one extra number beyond the ones my friend found. The reason my friend missed an integer is because my friend simplified their calculations by discarding any expression in which an intermediate result is not an integer. With this restriction, it was impossible for my friend to form the final integer.
Which extra integer did I find?
Using all of the numbers $2,3, 8, 9$ exactly once and any of the operations $+, -, *, /, \wedge$, which integer between 0 and 100 can only be formed by an expression with a non-integer intermediate value?