query: What does it mean for a set to have an exponent?
positive_passages.docid: 20187
positive_passages.text: What's the meaning of the exponent here?
negative_passages.docid: 102138
negative_passages.text: Why does $\sqrt{x^2}$ seem to equal $x$ and not $|x|$ when you multiply the exponents?
negative_passages.docid: 38636
negative_passages.text: A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
negative_passages.docid: 104274
negative_passages.text: Express $C$ interms of the sets $A_n$
negative_passages.docid: 37189
negative_passages.text: Exponent of a number is a square root?
negative_passages.docid: 145873
negative_passages.text: Let $X$ and $Y$ be finite sets. Then the set $Y^X$ is finite and $\#(Y^X) = (\#Y)^{\#X}$.
negative_passages.docid: 54497
negative_passages.text: Set Notation - Inclusion and Proper Inclusion
negative_passages.docid: 71653
negative_passages.text: Why is the Cartesian product of a set $A$ and empty set an empty set?
negative_passages.docid: 58076
negative_passages.text: Subgroup generated by a set
negative_passages.docid: 142267
negative_passages.text: If two sets have the same cardinality, then so do their power sets. Converse can't be answered?
negative_passages.docid: 130418
negative_passages.text: Is ${\{\emptyset,\{\emptyset\},\{\{\emptyset\}\},\{\{\{\emptyset\}\}\},...\}} $ a set?
negative_passages.docid: 3072
negative_passages.text: If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
negative_passages.docid: 132165
negative_passages.text: "Polynomials" with non-integer exponents
negative_passages.docid: 51434
negative_passages.text: What does the symbol $\subset\subset$ mean?
negative_passages.docid: 38727
negative_passages.text: Modular Exponentiation and Primes
negative_passages.docid: 155635
negative_passages.text: Why is the math for negative exponents so?
negative_passages.docid: 18634
negative_passages.text: Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$