If $2^4 - 2^3 = 2^3$ and $2^5 - 2^4 = 2^4$, then is below a rule of subtracting exponents with similar base and exponents which are just $1$ away from each other?
$$A^e - A^{e-1} = A^{e-1}$$
I will also like to get an visual intuition of why this works. Thanks.
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$\begingroup$For $A \ne 0$ we have:
$A^e - A^{e-1} = A^{e-1} \iff A^e=2A^{e-1} \iff A^e=2 A^e A^{-1} \iff 1=2 A^{-1} \iff A=2$.
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