# Tagged Questions

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### What is the general notation for the principal value of complex exponential?

It is general to distinguish the principal value of complex logarithm set by denoting it $Ln( z)$. Is there any general notation to distinguish the principal value of complex exponential? In complex ...
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Of the following, why is a usually considered true, and for what reason other than "tradition" and "more convenient"? a: ${x}^{y^z} = x^{(y^z)} \neq {(x^y)}^z$ b: ${x}^{y^z} = {(x^y)}^z \neq ... 2answers 50 views ### Power correct notation Ok, I know this may sound dumb, but I am trying to understand which is the correct (most beauty) notation for the power function${\rm pow}(f(x),n)$. This is the correct one:$[f(x)]^n$From ... 1answer 49 views ### Can we write$\sqrt[w]{z}=z^\frac{1}{w}$when both$w$and$z$are complex numbers? [duplicate] Let$w$and$z$be complex numbers defined in terms of real numbers$a$,$b$,$c$and$d$as follows: $$w = a+bi \\ z = c+di$$ Can we analogically write $$\sqrt[w]{z} = z^\frac{1}{w} \qquad ... 2answers 181 views ### How to evaluate powers of powers (i.e. 2^3^4) in absence of parentheses? If you look at 2^{3^4}, what is the expected result? Should it be read as 2^{(3^4)} or (2^3)^4? Normally I would use parentheses to make the meaning clear, but if none are shown, what would you ... 0answers 213 views ### Notation for n-ary exponentiation We have n-ary sums (\sum) and products (\prod). Is there an n-ary exponentiation operator?$$\underset{i=1}{\overset{n}{\LARGE{\text{E}}}}\, x_i = x_1 \text{^} (x_2 \text{^} (\cdots \text{^} ... 1answer 147 views ### Operators - sums, products, exponents, etc.$(x + x + \cdots + x)$, where$x$added$n$times can be written as$x * n$.$(x * x * \cdots * x)$, where$x$multiplied$n$times can be written as$x ^ n$. Is there an operator, such that if ... 5answers 399 views ### Can anyone explain why$a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}$I'm so puzzled about this: $$a^{b^c} = a^{(b^c)} \neq (a^b)^c = a^{(bc)}.$$ Why isn't$a^{b^c}$equal to$a^{(bc)}$? Why is$a^{b^c}$instead equal to$a^{(b^c)}$? And how is it possible that ... 1answer 676 views ### Why use radical notation instead of rational exponents? I'm helping my younger sister for her math class. She has recently been taught integer exponents, and has starteed studying radicals (mainly square roots). The next topic will be rational exponents, ... 2answers 77 views ### Exponentation vs Power What definition of$a^b$operation is the most popular and standartized: Exponentation or Power? Is any difference between them? 0answers 129 views ### Notation for Cartesian power, an oddity in the international standard The Cartesian product of$A$with itself$n$times is normally denoted using superscript notation$A^n$, and this what ISO 31-11 defined as standard. However, ISO 31-11 has been superseded by ISO ... 4answers 259 views ### What is the meaning of$\exp(\,\cdot\,)$? What is the meaning of the notation$\exp(\text{expression})$? I think that it's something of the form$a^\text{expression}$but does it mean that the base$a=e$or can it be any base? 3answers 175 views ### Mathematical function for the powers I have this formula $$\underbrace{2^{2^{2^{.^{.^{.^{2^2}}}}}}}_n$$i.e. where the total number of 2's is$n$. Is there any way to write it as a single mathematical function? 2answers 621 views ### Notation of inverse trigonometric functions and exponentiation [duplicate] Possible Duplicate:$\arcsin$written as$\sin^{-1}(x)$I have worked a bit on trigonometry today, and something strikes me as inconsistent. In the book, the notation for the inverse sine ... 3answers 628 views ### Who introduced the notation$x^2$? In the book 'Problem Solving and Number Theory' I read The law of quadratic reciprocity was discovered for the ﬁrst time, in a complex form, by L. Euler who published it in his paper ... 2answers 483 views ### Solving tricky Knuth Up Arrow Notations How would I solve something like$2\uparrow\uparrow n$? when n ≤1? Or$2\uparrow^{-2}2\$? Thanks!
If we have $$x^y = z$$ then we know that $$\sqrt[y]{z} = x$$ and $$\log_x{z} = y .$$ As a visually-oriented person I have often been dismayed that the symbols for these three operators ...