Final answer:
Under Dillon's Rule, 'Powers that would be convenient for the local government' are NOT a type of local government power. This rule emphasizes necessary and legally permitted powers rather than those merely convenient for local administrations.
Step-by-step explanation:
Under Dillon's Rule, the type of local government power that is NOT recognized is 'D) Powers that would be convenient for the local government.' Dillon's Rule is a legal principle that strictly limits the powers of local governments to those expressly granted by the state legislature, those implied from the powers expressly granted, and those indispensable for carrying out the government's purposes.
Powers given in expressed words, or expressed powers, are those directly outlined in a state's constitution or laws. Powers implied from these expressed powers allow local governments to perform functions that are not explicitly defined but are a logical extension of their express powers. Powers indispensable to government function refer to powers that are considered essential to perform the government's duties even if they are not expressly stated.
However, the concept of 'Powers that would be convenient' does not adhere to Dillon's Rule, as this rule does not account for the convenience of local governments but focuses on what is necessary and permitted under the law. This sharply contrasts with the home rule, where local governments are granted more autonomy and can exercise any powers not specifically prohibited by state law or charter.