The original code fails because the input() function returns a string, and the exponentiation operator () cannot be applied to a string operand, resulting in a TypeError. To resolve this, the string returned by input() must be converted (cast) to a numeric type before the calculation.

Both int() and float() can convert the string '10' into a number.

- Option B: int('10') results in the integer 10. 10 2.0 correctly calculates 100.0.

- Option D: float('10') results in the float 10.0. 10.0 2.0 correctly calculates 100.0.

Both options successfully prevent the TypeError and produce the desired output.

A. bool('10') evaluates to True. In an arithmetic context, True is treated as 1, so the calculation becomes 1 2.0, which results in 1.0, not 100.0.

C. complex('10') converts the input to a complex number, (10+0j). The result of the exponentiation is (100+0j), which is a complex type, not the required float 100.0.

1. Official Python Documentation: The input() function is documented to always return a string. For arithmetic operations, this string must be converted. "The function then reads a line from input, converts it to a string (stripping a trailing newline), and returns that."

Source: Python 3 Documentation, The Python Standard Library, §4.1. Built-in Functions, input(). (docs.python.org/3/library/functions.html#input)

2. Official Python Documentation: The numeric types int and float support the exponentiation operator (), while strings do not. Type conversion functions like int() and float() are necessary to convert strings to numbers.

Source: Python 3 Documentation, The Python Tutorial, §3.1.1. Numbers. (docs.python.org/3/tutorial/introduction.html#numbers)

3. University Courseware: MIT OpenCourseWare materials for introductory Python courses explicitly cover the necessity of casting the string result of input() to a numeric type like int or float before performing mathematical calculations.

Source: MIT OpenCourseWare, 6.0001 Introduction to Computer Science and Programming in Python, Fall 2016, Lecture 2: Objects in Python, Section on "Input/Output". (ocw.mit.edu)