This is not only a question that involves the rules of exponents but also min max scenarios

We have \(-2^x\) and we do know that regardless the value, the exponents is negative so we do know, first thing first , that when a number is raised to negative power we have a fraction

\(\frac{1}{-2^x}\)

Now we need to find two values, one min and one max, to have the difference.

From the properties of fractions, we also know that the smaller the denominator, the higher the overall fraction, and vice versa.


To maximize the value of the fraction our denominator must be small and the min value for x is 2ù

\(\frac{1}{-2^2}=\frac{1}{4}\)




Now we do the opposite

\(\frac{1}{-2^1}=-\frac{1}{2}\)


\(m-n\)

\(\frac{1}{4}-(-\frac{1}{2})=\frac{1}{4}+\frac{1}{2}=\frac{3}{4}\)

C is the answer