Exponentiation #3 - Same Base, Different Exponent! What is a^0 ? Mathematical Rule for a^n*a^m !
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- Опубліковано 9 чер 2024
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Today we derive the first rule of exponentiation! We are dealing with the case where we multiply the same base but different exponents together :) Also, we will thus find out, what a^0=1 evaluates to! Enjoy :3
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Papa flammy, the hive demands more.
yooo what a coincidence, I toke a walk today in the morning and thought about the derivation of the exponentiation too lol, although its trivial ig, its always a satisfying experience to derive it on your own
4:25 Let me repeat that part of the video a dozen times thank u
Papa! Consider doing the following video when you come back. Integrate e^x*sin(x), but do it by using e^x=cos(ix)-isin(ix), then product-to-sum formulas. Okay bye!
Suggestion: Do complex numbers in the Sets of Numbers series
Methmaticians
woohoo early to papa flammy video
Danke schön papa flammy . I learnt a new thing today
dankeschön is a single word
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Can you please show that a^n•a^m=a^(n+m) also works for irrational exponents where you cannot just write a^n as a•a•a…•a n times? For example for a^π•a^e?
Follows from the functional equation of the exponential function: a^x=e^(xlog(a))
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what is the height of a fluid inside a sphere when it occupies 1/4 of the sphere?
I'm sick too papa
make a video on glasser's master theorem plz?
Every Papa video is a must not Fa…Flam challenge. 🤪
Should’ve done a^n*a^l instead😏
where do you find these memes papa
share the source 🙏
in this case it looks like he is the memer
More about 100000000 years ago Richard Feynman already watched this video...
I want to point out a mistake in the proof that a^0=1
The power a^0 by definition is equal to 1. This cannot be proven.
First we need to know what a power with exponent 0 means before any proof can be done. Without knowing what a^0 means we cannot even use the symbol a^0.
The mistake in the proof is that you used the property (a^m).(a^n) =a^(m+n) in the case n=0 without knowing what a^0 means.
The definition a^n=a.a.a…a makes no sense if n=0 and for that another definition had to be given.
The property (a^m).(a^n) =a^(m+n) is first proved to hold for natural m , n >=1. To GENERALIZE this property so that it also applies in the case where n=0 , WE DEFINED a^0=1.
For the same reason WE DEFINED a^(-n)=1/(a^n) and we cannot do a proof of this equality before we know what a power with a negative exponent means. With this definition we can then prove that the property (a^m).(a^n) = a^(m+n) also holds for negative integers and not consider that it holds for negative integers and with the help of this to prove that a^(-n)=1/(a^n).
For the same reason (i.e. for the property (a^m).(a^n) = a^(m+n) to hold for rational exponents), WE DEFINED the power a^(1/n) = nth root of a etc.
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Based
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Where is the proof.