What is the proper notation for an infinitely repeating exponent?

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What is the proper notation for an infinitely repeating exponent? Such as:

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This is called tetration.

The notation $^n 3$ is used to stand for $3^{3^{3^\ldots}}$ with $n$ iterations.

Therefore your example would be $$x^{3^{3^{3^\ldots}}}=x^{^n 3}$$