Final answer:
The claim in the question is incorrect; the additive inverse of 4x² is actually -4x², not -4x⁻². Negative exponents indicate reciprocals rather than additive inverses.
Step-by-step explanation:
The statement 'the additive inverse of 4x² is -4x⁻²' is incorrect because an additive inverse is a number which, when added to the original number, will result in zero. The correct additive inverse of 4x² is -4x². When you add 4x² and -4x² together, the result is zero.
To clarify the terminology, negative exponents represent reciprocals, not additive inverses. For example, x-1 is equivalent to 1/x, and similarly, x-2 would be 1/x², not an additive inverse.