Why do negative powers mean 'one over x'?

Have you ever been told that "x to the negative power" means "one over x"? If so, it probably wasn't explained why! In this video, we show exactly why "x to the negative one power" means "one over x". It's easy!

In this video we look at negative exponents in math and explain exactly what they mean. If you've ever want negative exponents explained in a simple, clear and concise way, this is the video for you!

[memo]

When u discover how simple those reasons are and wonder why on earth only few teachers bothered explaining it...

[cbsteffen]

In summary, opposites (positive and negative) for exponents mean reciprocals for base numbers. That’s what we all have to keep in mind.

[TealComet]

Thank you ! It's not some mindless mantra I have to memorize anymore !!!

[ahmedal-ebrashy]

Not what I wanted but best thing I found cause no youtuber is explaining it

[rohitaryax-antse]

THANKYOU BRO VERY MUCH IM VERY TENSED ABOUT THIS DOUBT AND U SOLVE IT MAY GOD BLESS YOU ...LOVE FROM INDIA

[MegaSquiff]

Subscribed!…just what I’ve been looking for. A big thanks.

[kunedroid]

Oh mate, could you do one on the use of inverse numbers in formulas/derivation ? I mean, there are many places where I see the formula with an inverse number (1/x) being used to abstract a branch of the problem (I am just an IT nerd, don't know the actual math of anything nor their right names).
An example I used recently is when calculating parallel resistance and equivalent resistance in voltage divider circuits... But basically it seems it is being used to "sample" a 'unit' (a one) of a branch of the problem and use it to abstract (kinda like how much % do this branch contribute in the overall "system" (circuit in the example)).
I would love to see a more mathematical explanation, I couldn't find it yet...
Cheers!

[tostupidforname]

I personally think its easier to explain with the inverse property but this is also a good way

[prantosaha]

Here, I have a question that, can I use a mathemetical defination to prove an other defination?
For example, here you used x^0 =1. It's also a mathematical defination.
But is it fair to use to give another defination?

[waiqiao]

This doesn’t answer why, it just states another way of writing the same thing

[milton]

The issue here is that to prove that x^0 =1 you use the fact that x^(-1)=1/x which is exactly what you are trying to prove here which lead you to a circular issue of needing a previous result to prove one that you want to prove where the previous result need the current one to be proven.

[vishalsg]

I personally feel like u dont question mathematics. Its ridiculously tiring when u start to question what is happening and why.

[saburousaitoh]

It is right even the case x =0:


0/0=0 was known about 1300 years ago in India; now 0/0=1/0= tan(\pi/2)=0. However you have to find their definitions and meanings: viXra:1908.0100 submitted on 2019-08-06 20:03:01, (709 unique-IP downloads)



Fundamental of Mathematics; Division by Zero Calculus and a New Axiom

[bjorneriksson]

Im not sure how this explained the "why" ? It was mote a "how" demonstration but maybe thats the same in math that is kind of tautologic in nature.

[tailyanggambo]

Here the same problem arises. If there is no x⁰=1 then u can't proof x-¹ and if you don't have x-¹=1/x then u can't proof x⁰=1
I searched for x-¹ = 1/x proof without using x⁰=1 formula. I already know that.
Then tell us how x⁰=1😅
If there were no x-¹=1/x

[RohitSingh-lxck]

Such a great channel but still have only 6k followers ❤️.

[pelasgeuspelasgeus]

So, everything is based on the absurd x^0=1?

[abdulbaten]

But if *a* is a negative number, then the exponent becomes positive, right? Bcs Negative × Negative = Positive

[MohitBaboria]

Bro thos does not make any sense
Because x⁰/x¹ is same as x⁰ * (1/x⁰)
So you just rewrote the same thing which we had to prove

[dikeshgaming]

Look at the fourth step you are using (the x^-1=1/x) to prove itself, this method is wrong