Partial answer with "simple" operators:
>! (10 + 10) / (10 + 10) = 1  
>! (10 / 10) + (10 / 10) = 2  
>! (10 + 10 + 10) / 10 = 3  
>! ((10 / 10) + (10 / 10))² = 4  
>! (10 * 10) / (10 + 10) = 5  
>! ((10 + 10 + 10) / 10)! = 6 (thanks to [Kepotx][1])  
>! 10 10 10 10 = 7  
>! ((10 / 10) + (10 / 10))³ = 8  
>! ((10 * 10) - 10) / 10 = 9  
>! 10 + (10 - 10) * 10 = 10  


  [1]: https://puzzling.stackexchange.com/users/44790/kepotx