query: Questioning the commutative property in complex powers
positive_passages.docid: 19945
positive_passages.text: For complex numbers $a,b,c$, explain why $a^{b\cdot c}=(a^b)^c$ is not necessarily true.
negative_passages.docid: 127304
negative_passages.text: Understanding the algebra of polynomials on a linear space
negative_passages.docid: 66134
negative_passages.text: Sufficiently many idempotents and commutativity
negative_passages.docid: 93681
negative_passages.text: Integral closure of $\mathbb{Z}$ in $\mathbb{C}$ is not finitely generated as a $\mathbb{Z}$-module?
negative_passages.docid: 10254
negative_passages.text: Is the Polynomial Factor Theorem true over all commutative rings?
negative_passages.docid: 97800
negative_passages.text: Exterior power "commutes" with direct sum
negative_passages.docid: 68255
negative_passages.text: Theorems in complex analysis.
negative_passages.docid: 38346
negative_passages.text: Commutative Ring: Nilpotent elements closed under addition?
negative_passages.docid: 138360
negative_passages.text: Exponents and absolute value w/ complex numbers
negative_passages.docid: 38130
negative_passages.text: Complex structure on $\mathbb{C}\mathbb{P}^2\# \dots \# \mathbb{C}\mathbb{P}^2$
negative_passages.docid: 136872
negative_passages.text: Why uniform closure $\mathscr{B}$ of an algebra $\mathscr{A}$ of bounded complex functions is uniformly closed?
negative_passages.docid: 105170
negative_passages.text: About product of $k$ commutators
negative_passages.docid: 46144
negative_passages.text: Understanding imaginary exponents
negative_passages.docid: 35222
negative_passages.text: Characterizing units in polynomial rings
negative_passages.docid: 50057
negative_passages.text: Complex analysis and Cauchy Residue theorem
negative_passages.docid: 118911
negative_passages.text: Classifying Unital Commutative Rings of Order $p^2$
negative_passages.docid: 71822
negative_passages.text: Commutator algebra in exponents