seems you just copied the lines somewhere and don't know what f means here.
well, it should be a pure funtion object, please reference to ref/Function   
CloudDeploy[
 FormFunction[{"basis" -> <|"Interpreter" -> "Number", "Input" :> 3|>,
    "exponent" -> <|"Interpreter" -> "Number", "Input" :> 2|>}, 
  #basis^#exponent &, 
  AppearanceRules -> <|"Title" -> "demo power function", 
    "Description" -> "Enter two number as prompted below"|>, 
  FormTheme -> "Red"]]
good luck.