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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Exponent, Index or Power ... what do you call it?

If you have, for example, 5[sup]4[/sup], what do you call the "4" ?

(I am working on a page and want to use the most widely accepted word)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,336

Power is the most common of the three. Exponent and Index are also used. Both are mathematical terms. To the layman, power is the simplest. I think, it is accepted by mathematicians too. If the page is meant for students and mathematicians, however, my choice would be **exponents**. Aren't we familiar with the laws of exponents and exponential growth ?

Character is who you are when no one is looking.

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**justlookingforthemoment****Moderator**- Registered: 2005-05-26
- Posts: 2,161

All three!

Different uses:

5 to the power of 4; Index Laws; exponential notation

However, I would probably lean towards calling the '4' the exponent.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

And also ... how would you say 5[sup]4[/sup] (in words)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,336

5 to the power 4, 5 raised to 4, the fourth power of 5 etc.

Its difficult to find exponent and index in general use.

Character is who you are when no one is looking.

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

I would just say "5 to the fourth."

And yeah, when they first taught me of exponents, they called them powers. Except when they used the pneumonic, "Please Excuse My Dear Aunt Sally," to help us remember the order of operations. (That's Parenthesis Exponent Multiplication Division Addition Subtraction, for the uninitiated.)

I've never heard them called indexes.

*Last edited by ryos (2006-02-27 04:05:21)*

El que pega primero pega dos veces.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

That's because they're called indices.

I normally call them powers as well. Wait, that's a lie. I *always* call them powers.

I use the term 'exponential growth/decay', but that's different.

For your page, I would have 'powers' as the main title, but include the other two as well as part of the page, just saying that they can also be used.

I would say '5[sup]4[/sup]' as "Five to the four." Possibly incorrect, but everyone knows what I mean.

Also, if you use the [su(p/b)] tags on the last line of a post, then the bottoms of the words get cut off. That's why this sentence is here.

Why did the vector cross the road?

It wanted to be normal.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I just wanna say that the indexes are usually low, not up.

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

OK, I have done the pages. I went for "Exponent" because of the "Laws of Exponents".

The page on Exponents

And the page on Laws on Exponents

Any mistooks?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Love it! Nice lessons on exponents.

Don't forget google, 10^100.

I never realized they had so many numbers named up to 10^63.

That's great, and if you take the number associated with the

prefix, like 2 for bi (billion), add 1 and multiply by 3, you get the 10^number.

Like the 10^63 one is a "V" word, which is like the "v" in 20 in French and

(20+1)*3 is 63.

I never thought about the positive and negative exponents as a

continuous development, that is really awesome! The multiplying and

dividing and passing through the 1. Very nice lesson.

**igloo** **myrtilles** **fourmis**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,336

Very good, MathsIsFun. I didn't notice any mistakes when I rushed through the pages.

Character is who you are when no one is looking.

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**ryos****Member**- Registered: 2005-08-04
- Posts: 394

Nice pages! I only found one mistake. The comma in this sentence, is superfluous:

The "Laws of Exponents" (also called "Rules of Exponents"), all come from three ideas:

El que pega primero pega dos veces.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

John E. Franklin wrote:

Love it! Nice lessons on exponents.

Don't forget google, 10^100.

Google is the popular search engine.

Googol is the number.

Don't feel bad, it's a very common mistake.

And as others have said, great pages, Rod! Very well explained.

Why did the vector cross the road?

It wanted to be normal.

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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

Can you do a page on triangular numbers please rod.I keep trying to find the formula and in the end my dad told me but I FORGOT sob sob.Please.

Presenting the Prinny dance.

Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Thanks guys!

(Apparently "googLE" was a mistake when they registered the domain name.)

And espeon - I have a small section on triangular numbers on this page, and they also are part of Pascal's Triangle.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

And there was something like

googolplex=10^(10^100) means 1 with one googol 0-s after it.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Isn't there something for non-integer exponents:

IPBLE: Increasing Performance By Lowering Expectations.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

That's an interesting problem, krazzi. I tried relating it to

, but I didn't get very far.And you're right about the googolplex being 10^googol.

There's also the googolplexian, which is 10^googolplex.

Why did the vector cross the road?

It wanted to be normal.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

is actually real. And it is:

cosh(Pi/2)-sinh(Pi/2)=

0.2078795763507619085469556198349787700338778416317696080751358830554198772854\

821397886002778654260353405217733072350218081906197303746639869999112631786412\

057317177795200674337664954224638192973743053870376005189066303304970051900555\

620047586620529435183443184345502747974534476993471417238323081527148180076092\

107419204715187835348958482189018602958233129566295207082340956769636374203945\

143939418386190108082089777175170500434817645475171452989434113414201756221548\

809541992091473585152856795345269763049937295772948259970284775240324808207770\

291871972175383475208608648587534778655469838325536790138351722118641519595912\

039044480226696736794359650205584360295696065582494313369401729524289610861619\

824999045135690057364051102664391373517406279074968849012275571917762037730358\

452877575760349503812991539865873765359168640051599889710637990616086300309901\

364570949813814380366403489134562875716779926337700074958934442398029209326823\

063252497856169693490834025947248477168094655354769168600552152102...

cosh(Pi/2)-sinh(Pi/2)=

0.2078795763507619085469556198349787700338778416317696080751358830554198772854\

821397886002778654260353405217733072350218081906197303746639869999112631786412\

057317177795200674337664954224638192973743053870376005189066303304970051900555\

620047586620529435183443184345502747974534476993471417238323081527148180076092\

107419204715187835348958482189018602958233129566295207082340956769636374203945\

143939418386190108082089777175170500434817645475171452989434113414201756221548\

809541992091473585152856795345269763049937295772948259970284775240324808207770\

291871972175383475208608648587534778655469838325536790138351722118641519595912\

039044480226696736794359650205584360295696065582494313369401729524289610861619\

824999045135690057364051102664391373517406279074968849012275571917762037730358\

452877575760349503812991539865873765359168640051599889710637990616086300309901\

364570949813814380366403489134562875716779926337700074958934442398029209326823\

063252497856169693490834025947248477168094655354769168600552152102...

IPBLE: Increasing Performance By Lowering Expectations.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Gosh! You would think this value may have some magical properties.

Anyway, I have added a footnote to the Laws of Exponents page about powers of 0, and particularly 0[sup]0[/sup]. Do you think it is a fair summary of it?

I have also made a page about fractional exponents. I wish I could explain it more simply. Anyway, please have a look at Fractional Exponents and give me any corrections (Algebra students world-wide will be thankful if you can improve the page)

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,336

MathsIsFun wrote:

Gosh! You would think this value may have some magical properties.

Anyway, I have added a footnote to the Laws of Exponents page about powers of 0, and particularly 0[sup]0[/sup].

In most cases, though, you can assume that

Fractional Exponents has been neatly explained on the page. Every possible case has been explained.

If it is not out of place, the exponents page may include the facts that

(i) the maximum value of xth root of x for any value of x is 1.444667861 approximately, obtained when x=e, the natural logarithm base, approximately, 2.7182818284.

(ii) the maximum value of x^x^x^x....ad infinitum for any value of x such that the resultant is finite is the same value given above, viz. 1.444667861 and the result tends to e.

It can be shown that 2^2^2^2^2....is an alarmingly big number when the tower of exponents is just 5 steps high!

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Nice pages, MathsIsFun!

I especially liked the graphing tool. A minor gripe is that it doesn't fully plot if you go to the extremes, like x[sup]-40[/sup]. And it also goes a bit crazy if you try x[sup]something/0[/sup], but that's to be expected. Overall, very nice and well explained pages!

Why did the vector cross the road?

It wanted to be normal.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,306

I like to graph...

**X'(y-Xβ)=0**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,560

Great!

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