My pal and I are every making an attempt to kind the integers from $0$ to $100$ utilizing the numbers $2, 3, 8, 9$. We are solely allowed to make use of the 5 fundamental operations: addition, subtraction, multiplication, division, exponentiation, in addition to parentheses. No concatenation is allowed.

After we work on the issue for some time, I discover 89 totally different integers, whereas my pal solely finds 88 totally different integers. We evaluate our work, and we understand that I discovered one further quantity past those my pal discovered. The cause my pal missed an integer is as a result of my pal simplified their calculations by discarding any expression during which an intermediate outcome isn’t an integer. With this restriction, it was unattainable for my pal to kind the ultimate integer.

Which further integer did I discover?

Using the numbers $2,3, 8, 9$ and the operations $+, -, *, /, wedge$, which integer between 0 and 100 can solely be shaped by an expression with a non-integer intermediate worth?