For natural a, we define ba as ∏(b) a times, but for any real a and positive real b, we define ba = exp(a*ln(b)). Answer from Deleted User on reddit.com
exponent
/ĭk-spō′nənt, ĕk′spō″nənt/
noun
- One that expounds or interprets.
- One that speaks for, represents, or advocates. Our senator is an exponent of free trade.
- (Mathematics) A number or symbol, as 3 in (x + y)3, placed to the right of and above another number, symbol, or expression, denoting the power to which that number, symbol, or expression is to be raised.
Merriam-Webster
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Definition of EXPONENT
January 28, 2026 - The meaning of EXPONENT is a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power. How to use exponent in a sentence. Did you know?
Dictionary.com
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EXPONENT Definition & Meaning | Dictionary.com
A number or symbol, placed above and to the right of the expression to which it applies, that indicates the number of times the expression is used as a factor. For example, the exponent 3 in 5 3 indicates 5 × 5 × 5; the exponent x in (a + b) x indicates (a + b) multiplied by itself x times.
BYJUS
byjus.com › maths › exponent
Exponent Meaning
As defined above, the exponent defines the number of times a number is multiplied by itself. The power is an expression that shows repeated multiplication of the same number or factor.
Published November 3, 2021 Views 17K
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Intro to exponents (video)
What is the definition of an exponent?
For natural a, we define ba as ∏(b) a times, but for any real a and positive real b, we define ba = exp(a*ln(b)). More on reddit.com
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June 28, 2022exponentiation - Formal definition of numbers with real exponents - Mathematics Stack Exchange
What is the definition of $a^{b}$, where $a,b\in \mathbb R$. ... $\begingroup$ I've edited your title and a bit of your question to reflect what I think you're really asking. $\Bbb R$ is real numbers. If you really wanted to ask about rational exponents, that would be $a, b \in \Bbb Q$. But ... More on math.stackexchange.com
What is the actual mathematical definition of exponentiation?
(1) It is defined that ba = ea×ln(b) . (2) ex is defined as the so called "taylor series": ex = x⁰/0! + x¹/1! + x²/2! + x³/3! + ... and ln(x) is defined as the inverse function of ex . (3) Every power that shows up in the series is simply defined by repeated multiplication since those are integer powers. More on reddit.com
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March 4, 2024[pre-calc] Definition of rational exponents.
It should be obvious why it would be convenient. Larger roots and exponents are more complicated and difficult to describe or analyze.
I'm not completely certain, but I believe it is only required if the common factor would be a multiple of 2. The reason for this is because even roots can never accept a negative input (at least in the real numbers) and even exponents always give a positive output. For example, (-8)2/6 = (-8)1/3 = -2. But ((-8)2 )1/6 = (64)1/6 = 2. And (-81/6)2 is undefined because the 6th root can't accept -8. So rational exponents with common factors are defined, but you have to simplify the fraction before you can convert it otherwise you might get a different answer.
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March 23, 2015What is an Exponent?
Exponent is the method of expressing large numbers in terms of powers. For example, 5 multiplied 3 times, i.e. 5 × 5 × 5 can be expressed as 5^3, where 3 is the exponent of 5.
byjus.com
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Exponent Meaning
What is 2 with an exponent of 4?
2 with an exponent of 4 can be written as 2^4 and its value is 2 × 2 × 2 × 2 = 16.
byjus.com
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Exponent Meaning
What is the zero exponent rule?
Zero exponent rule states that any number with an exponent zero (0) is equal to 1.
byjus.com
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Exponent Meaning
Cambridge Dictionary
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EXPONENT | definition in the Cambridge English Dictionary
The parameterp is the exponent in the non-saturated regime, whiles is the exponent for the situation where saturation is present. ... The particular choice of exponents changes the response characteristics but is proven to keep the system stable.
Esri Support
support.esri.com › en-us › gis-dictionary › exponent
Exponent Definition | GIS Dictionary
[mathematics] A number that indicates how many times a base value is multiplied by itself. Exponents are usually indicated with superscripts.
Reddit
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r/learnmath on Reddit: What is the definition of an exponent?
June 28, 2022 -
Hello everyone! I was wondering what the formal definition of an exponent is. I’ve made it through calc 2 and up until now the only detention I’ve received is either an is a multiplied by itself n times or given am/n would be the nth root of am, for example sqrt(a) is a1/2. However I was wondering if there is a more formal definition. For example, 2pi can be computed, but wouldn’t work with the above definitions, as you can’t multiply 2 pi times and pi is an irrational number.
Any insight on this would be much appreciated!
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For natural a, we define ba as ∏(b) a times, but for any real a and positive real b, we define ba = exp(a*ln(b)).
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As other commenters have made clear, there are several different answers to this question. No matter which approach you choose, there are theorems that need to be proved in order for the definition to be coherent. For example, if you take u/Crafty_Potatoes 's definition, you have to prove that this definition of exponentiation preserves the properties we like, for example, aman = am+n. This kind of thing will be true of any definition you adopt. Similarly, you should definitely believe u/thecooIestperson about the definition of exp, but again, you will want to prove that, essentially, exp(x) = er for r rational and e is a single well-defined constant. If you adopt u/bluesam3 's definition, your soul will be unsatisfied unless you prove that it implies u/thecooIestperson 's series identity. Vice versa, too. Even u/ConservatoryCanine 's definition incurs a theoretical debt: to prove that the exponential identities are true, and that the definition is coherent (as they acknowledge in their comment).
Collins Dictionary
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EXPONENT definition in American English | Collins English Dictionary
These examples have been automatically selected and may contain sensitive content that does not reflect the opinions or policies of Collins, or its parent company HarperCollins. We welcome feedback: report an example sentence to the Collins team. Read more… Common-good exponents argue that public officials should be guided by considerations of goodness and fairness that most all of us recognize in personal conduct.
Mathnasium
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What Is an Exponent in Math? A Kid-Friendly Definition
Exponent is the power to which a base is raised. Power is the value of a number raised to some exponent.
Math is Fun
mathsisfun.com › definitions › exponent.html
Exponent Definition (Illustrated Mathematics Dictionary)
Illustrated definition of Exponent: The exponent of a number says how many times to use that number in a multiplication. It is written as a small...
Wikipedia
en.wikipedia.org › wiki › Exponentiation
Exponentiation - Wikipedia
February 2, 2026 - The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power. The word "raised" is usually omitted, and sometimes "power" as well, so 35 can be simply read "3 to the 5th", or "3 to the 5". The exponentiation operation with integer exponents may be defined directly from elementary arithmetic operations. The definition of the exponentiation as an iterated multiplication can be formalized by using induction, and this definition can be used as soon as one has an associative multiplication:
EtymologyHistoryTerminologyInteger exponentsRational exponentsReal exponentsComplex exponents with a positive real baseNon-integer exponents with a complex baseIrrationality and transcendenceInteger powers in algebraPowers of setsRepeated exponentiationLimits of powersEfficient computation with integer exponentsIterated functionsIn programming languages
Cuemath
cuemath.com › algebra › exponents
Exponents - Definition, Examples | Properties of Exponents
The exponent of a number shows how many times a number is multiplied by itself. For example, 34 means 3 is multiplied four times by itself, that is, 3 × 3 × 3 × 3 = 34, and here 4 is the exponent of 3. Exponent is also known as the power of a number and in this case, it is read as 3 to the ...
Brighterly
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What is Exponent ⭐ Definition, Properties, Examples, Facts
January 5, 2024 - An exponent is a mathematical notation used to express how many times a number, called the base, is multiplied by itself. The exponent is written as a small number positioned above and to the right of the base. For example, in 3^4, 3 is the base and 4 is the exponent.
Iacedcalculus
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Understanding the Definition of Exponents - iacedcalculus.com
November 8, 2024 - An exponent is a small number placed above and to the right of a base number, indicating how many times to multiply that base by itself.
SplashLearn
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What is Exponent? Definition, Properties, Examples, Facts
March 15, 2024 - In short, power or exponent indicates the number of times a number needs to be multiplied by itself. Here, the base can be any integer, fraction or decimal.
Columbia University
columbia.edu › itc › sipa › math › exponents.html
Exponents
An exponent is a number or letter written above and to the right of a mathematical expression called the base. It indicates that the base is to be raised to a certain power. x is the base and n is the exponent or power. Definition: If x is a positive number and n is its exponent, then xn means ...
Encyclopedia Britannica
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Exponent Definition & Meaning | Britannica Dictionary
EXPONENT meaning: 1 : someone who supports a particular cause, belief, etc.; 2 : someone who is known for a particular method, style, etc.
YouTube
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WHAT IS AN EXPONENT IN MATH? - YouTube
On this lesson, you will learn what is an exponent in math and the exponent definition. For more MashUp Math content, visit http://www.mashupmath.com and joi...
Published September 21, 2015 Views 73K
Vocabulary.com
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Exponent - Definition, Meaning & Synonyms | Vocabulary.com
You may already know the mathematical meaning of exponent: a numeric notation showing how many times a number is multiplied by itself. How did exponent come to mean a strong advocate or promoter of something?