My son mistaken to answer his math question: $2^{-x} = 0.5^{x}$ He said this must be false, I asked ChatGpt but still not satisfied with the answer because I want to explain to my son at age 12.
The strange part is: when you look at $2^{-x}$ the result of Y must be negative while $0.5^x$ is positive.
On
The main part of $2^{-n}$ is to understand $2^{-1}.$ $a^{-1}$ is generally the solution of the equation $a\cdot x=1,$ i.e. the inverse element to $a$ with respect to multiplication. $x=a^{-1}$ is how we write this element. Hence, $2^{-1}$ solves $2\cdot x =1$ which makes $2^{-1}=\dfrac{1}{2}.$ Finally, $$ 2^{-n}=\left(2^{-1}\right)^n=\left(\dfrac{1}{2}\right)^n=0.5^n=\dfrac{1}{2^n}>0 $$
Hint:
$$a^{-b} = \dfrac {1}{a^b} = \bigg ( \dfrac {1}{a} \bigg )^b$$ See also Robert Israel's comment.