The second argument to FormFunction is function that expects a single Association (as is also true of APIFunction). The arguments coming to the FormFunction are available as named slot parameters, written like #Basis. It is not recommended to use uppercase letters to begin symbols, so I would also rename your FormFunction parameters to begin with a lowercase letter. Based on I would rewrite your code as follows:

simpleFunc[basis_, exponent_] := basis ^ exponent
foFuSiFu = FormFunction[{"basis" -> "Number", "exponent" -> "Number"}, simpleFunc[#basis, #exponent]&]

I did copy your version and this still does not work in my notebook in Wolfram Cloud. When I enter values into the form and try to evaluate it with

foFuSiFu[]

it gives me an error every time.

"The server is experiencing unexpected issues and could not process your request. Please try again in a few minutes."

When I do not use uppercase variables I would also need to change the name shown in the CloudDeploy. How do I change the label shown in the deployed form? (The examples in the documentation center have uppercase Variables to achieve that, which brought me to doing it that way to)