Explain why $((CH_3)_3C)^+$ is more stable than $(CH_3CH_2)^+$ and $(CH_3)^+$ is the least stable carbocation.

(N/A) The stability of carbocations is primarily determined by the inductive effect and hyperconjugation.
In $((CH_3)_3C)^+$,there are $9$ $\alpha$-$C-H$ bonds available for hyperconjugation,which provides significant stabilization.
In $(CH_3CH_2)^+$,there are only $3$ $\alpha$-$C-H$ bonds available for hyperconjugation,making it less stable than the tertiary carbocation.
In $(CH_3)^+$,there are no $\alpha$-$C-H$ bonds available for hyperconjugation. Furthermore,the vacant $p$-orbital is perpendicular to the plane of the $C-H$ bonds,preventing any overlap. Thus,$(CH_3)^+$ lacks hyperconjugative stability and is the least stable.