What is an exponent of an exponent called?

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I came across an expression of Stretched Exponential Decay $L/L_0 = \exp\left[-\left(\frac{t}{\tau}\right)^\beta\right]$, and got curious. Is there a term to refer to an exponent of an exponent? To be more specific, is there any proper name for $z$ in $x^{y^z}$?