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!

]]>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!

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)

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

0.2078795763507619085469556198349787700338778416317696080751358830554198772854\

821397886002778654260353405217733072350218081906197303746639869999112631786412\

057317177795200674337664954224638192973743053870376005189066303304970051900555\

620047586620529435183443184345502747974534476993471417238323081527148180076092\

107419204715187835348958482189018602958233129566295207082340956769636374203945\

143939418386190108082089777175170500434817645475171452989434113414201756221548\

809541992091473585152856795345269763049937295772948259970284775240324808207770\

291871972175383475208608648587534778655469838325536790138351722118641519595912\

039044480226696736794359650205584360295696065582494313369401729524289610861619\

824999045135690057364051102664391373517406279074968849012275571917762037730358\

452877575760349503812991539865873765359168640051599889710637990616086300309901\

364570949813814380366403489134562875716779926337700074958934442398029209326823\

063252497856169693490834025947248477168094655354769168600552152102...]]>

And you're right about the googolplex being 10^googol.

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

]]>

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

(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.

]]>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.

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

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.]]>