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This is an interesting question that mathematician, math experts and intelligent math student use the sign ^ for write raise to power. It is just because it is easer for typing in computer, use less space, use best for email and mobile text message.
n (x)^n = x Read as (x raise to power n)
Software Engineers are very fimiliar with the sign ^ because of use in calculation devices, computer and mobiles applications etc.
1/3 -2/3 2n - 2n -------------- = ? -2/3 2n
_____________________ / _____________ / / ____ / / / 2 / 4 / 4 . / 4 / \/ \/ / -------------------- / 3 \/ 2