query: For what values does $x^{x^{x^{x^{.^{.^{.}}}}}}$ make sense
positive_passages.docid: 15885
positive_passages.text: Infinite tetration, convergence radius
negative_passages.docid: 38636
negative_passages.text: A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
negative_passages.docid: 56745
negative_passages.text: Why does this not work with an imaginary exponent?
negative_passages.docid: 60769
negative_passages.text: How to solve x^x = const?
negative_passages.docid: 113345
negative_passages.text: Why do we set $x^0 = ct$ instead of $x^0 = t$?
negative_passages.docid: 37189
negative_passages.text: Exponent of a number is a square root?
negative_passages.docid: 25772
negative_passages.text: Limit of ${x^{x^x}}$ as $x\to 0^+$
negative_passages.docid: 114220
negative_passages.text: Find the value of $\large i^{i^{.^{.^.}}}$
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 50041
negative_passages.text: Significance of $\sqrt[n]{a^n} $?!
negative_passages.docid: 142725
negative_passages.text: The general solution of $x^a = a^x$ for real $a >0$
negative_passages.docid: 24980
negative_passages.text: What is the order when doing $x^{y^z}$ and why?
negative_passages.docid: 118314
negative_passages.text: How to define $x^a$ for arbitrary real numbers $x$ and $a$
negative_passages.docid: 106308
negative_passages.text: how do you solve $x^x=x$
negative_passages.docid: 46144
negative_passages.text: Understanding imaginary exponents
negative_passages.docid: 72620
negative_passages.text: Finding the value of $1.1^{82}$ using $(1+x)^{82}$ to a certain accuracy
negative_passages.docid: 102138
negative_passages.text: Why does $\sqrt{x^2}$ seem to equal $x$ and not $|x|$ when you multiply the exponents?