Maths isn't about just itself.. Maths is something which is beyond your perception I guess.. Loving maths is good but best when u know it's implications..
Thank you! Instead of just having to remember a rule, now I'll never forget that raising a number to the zero power = 1 because of the LOGIC behind it. The world needs good math teachers like you!
I'm with the girl on this one. Like her, yes, I understand why the rules of math mean x^0 = 1. But there is no real intuitive explanation here as to why this is so. When she asked for that, you just repeated the rules of math to explain it. I think she understands that x^y/x^y = 1, and that x^y-y = x ^ 0. What she wants t know is how to interpret this in the physical world. Can you give a physical example?
Had to write an algorithm in Python using this concept, if any number is raised to the power of zero - this explanation helped me fix some bugs. Thank you Brian from 9 years ago, appreciate it
I just started learning python yesterday. I already know some web development, I have learned in the past CSS, SASS, JavaScript, jQuary, how to use npm, git, grunt and webpack, and I have also learned mySQL, now I decided to learn python so that I can hopefully start understanding how backend works better and create web applications in the future. Front end is kind of annoying actually, I suck as CSS, so I want to become a back end developer. I however haven't really decided what I want to do yet, I just learn things that may be useful in the future, I was also interested in hacking so I learned some basic stuff about networking but I haven't yet learned anything about hacking because I didn't have the time. I also had studied logical gates once and made a calculator that could add and substract, I was planning to make a full ALU but gave up eventually because I had other stuff to do.
To help explain the person question some more. x^5/x^2 is essentially x*x*x*x*x/x*x We know that if a the same thing in the numerator is in the denominator then it cancels out. This would leave you with 2 x’s canceled at the bottom and top. But that leaves 3 x’s on the top. So, You had 5 x’sat the top and 2 x’s at the bottom but after canceling those x’s out you’re left with 3 x’s. That’s why you have to subtract exponents. Tbh I’m only explaining this so it can stick in my head better.
Finally, a video that actually EXPLAINS how X to the power of zero is 1. All the other videos say that they will EXPLAIN but they don’t explain anything they just say that X over X equals 1. This guy ACTUALLY explains it with the a - b analogy.
Is there any way to explain this without the dividing exponents rule? For me explaining a rule of math "x^0=1" using another rule of math does not help me actually understand it. Still just sounds like your saying it makes sense bc it's the rule.
This is a very intuitive reply. If an exponent is simply the number of times the base is a factor...well by definition, a factor has to be multiplied by something. So 5 to the first power means 5 as a factor once... But if it is a factor... It has to be multiplied by another factor. That other factor is the implied 1. So 1 x 5 = 5. So 5^0 Means there is a factor, but not any 5. So then you just have the implied 1 as a factor. And since 1 by itself has no other factors, only 1 can stand alone. The rule mentioned doesn't really explain why a number to the 0 power is one. It's just the unsimplified form...
It's very interesting to hear everyone explain this. Many people are able to make the connections on why it's intuitively 1 (like what you've done here) as well as if you look at (for example) 2^4 = 16, 2^3 = 8, 2^2 = 4, 2^1= 2, 2^0=1 and how you're dividing by 2 each step you go, but I guess it just seems bizarre when you think about what exponent is and you think '5 time itself zero times equals...1' Thanks for offering up a different explanation than normal though!
This helped me understand this alot better. I know the rule ,but I didn't understand why the rule works. Our teacher just told us what rule is instead of why it's that way. Thank you.
I get the rule but like if an exponent is the base times the exponent so X times 0 it should be 0, what bugs me is if you are using math to as an example backup a theory in idk lets say theorical physics and you use this rule to come up with matter out of nowhere it just wouldn't make much sense under some situations
I have always found the exponent rules to be intriguing. Intuitively, if someone were to ask me what is 5^0, I would just tell them 5; knowing that an exponent tells you how many times you should multiply a value/variable/expression by itself, if you asked me what 5^0 was, I would tell you to multiply 5 by itself 0 times, meaning don't multiply at all, and you are left with 5. I'm not sure how to get around that. :(
Shean Crane Not multiplying at all basically means we get 1 as whenever we multiply any number n times we start off with 1 and then multiple n times hence if we don’t multiply at all, we’re basically left with just 1.
The 0 power means that you're not multiplying by anything or you're dividing the number by the same number itself, which is always to equal to 1 as long as the number is not zero. When I mean you're not multiplying by anything, it's saying that there is an invisible 1 that nobody writes because 1 multiplied by any number is number itself. Let's say 5^3=1*5*5*5. As you go backwards by canceling out the 5's until you reach 5^0, you will get 1.
@@justabunga1 is the 1 multiplied in your example because there is always an invisible 1 under every number? then when we multiply we must multiply it by it’s reciprocal being 1/1 which equals 1 i.e. (5/1)^3 -> 5^3 = 5*5*5*1/1?
@@AnthonyTurcios no, the "1" that is being multiplied by any number just leaves that number unchanged. That is called a multiplicative identity. Therefore, any non-zero number raised to the power of 0 is always equal to 1. Take for example, 2^4=2*2*2*2=16. If we count down the powers of exponents until 0, then the problem arises. That's why there is an invisible 1 there. 2^4 is supposed to be the same as 1*2*2*2*2 if you notice that there is a 1 being multiplied from there and then 2 four times. That's why no one writes the 1 there.
Positive exponents are about repeated multiplication while negative exponents are about repeated division. That's it and it's enough. But some twisted mathematicians had to make it weird. The x^0=1 is not needed and it goes against the very definition of exponent which clearly states "The exponent of a number says how many times to use the number in a multiplication". So, if the power is 0 what should be the result based on the definition?
It’s actually any non-zero number raised to 0 power is always equal to 1. If it’s 0^0, the answer is indeterminate. When you deal with limits using calculus i.e. l’Hopital’s rule, you will have to do more work since it’s one of the 7 indeterminate forms.
I’m in Calc 2 right now and have never really known why this is true, only that it is. When you think of it that way, it really is quite simple. Is this also why 0^0 is indeterminate? Because it would simply simplify to 0^1/0^1 =0/0 = undefined?
I get the reason behind the explanation. I think it's the order of logic that makes this confusing still to me and others. It sounds like dividing exponents must be known before one can understand the one equation in understanding exponents (e.g. before one can learn what '9' is one must study division). It was explained best by a prior comment: (essentially) mathematicians did not have a definition for x^0, so to make sense of the concept, they used principles of other formulas such as the exchangeable properties in addition and the formula for division.
That's a good explanation of why this is so. When learning math concepts there is a large bit of acceptance that a student needs to be willing to give, the same is true with language use and learning, and Id say with most thing we do in life. If a student wants to know why a concept is than they need to look to the proofs for that concept and also I guess understand that math is both art and science and used in applications but for the science part it is trusted that if a concept is shown to be true than that is the accepted reality for the moment and people just go with that. As a real application of this concept, computers use this idea in constructing a binary number and this is an example of an application of this accepted concept. I may be right, I may be wrong, but that is my comment on this at the moment.
Anna Pritchard there’s an invisible 1 that nobody writes because of the multiplicative identity since 1 times any number is any number. From your example, x^2=1*x*x. Then, x^1=1*x. What is x^0? The answer is 1 as long as x is not 0 since 0^0 is indeterminate. The 0 power means that you’re not multiplying x by anything. I know it sounds like it doesn’t sense, but you will get the logic of how it works.
multiplying no numbers at all should give the multiplicative identity. Now, what's the multiplicative identity? Well, it's the only number which can be multiplied by any other number without changing that other number. In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
@@SixmillyJ That's correct. Raising to the 0 power means that you're not multiplying any numbers. It's the invisible 1 that nobody writes because of the multiplicative identity, which says any number multiplied by 1 is the number itself. You can also think of it as dividing the number by the same number, which is always equal to 1 as long as that number is not 0. For example, 4^6=1*4*4*4*4*4*4. When you cancel out the 4's until you reach 4^0, you get 1.
I think it's still doesn't make much sense. Not blaming the professor, but the rule itself. 5/5, 10/10 or a number divided by itself is always one obviously, but 5 by itself is 5, or a number by itself is just that number. Why would it be 1 if you have it to the exponent zero, but there is no division?
There's another way that you can think of since that is correct by the way. The 0 power means that you're not multiplying by the number itself. It's the 1 that is being multiplied since it's not written and nobody writes that because of the multiplicative identity, which says that 1 times any number is the number itself. Let's say 9^5=1*9*9*9*9*9. When you cancel out the 9's until you reach 9^0, all you have left is 1.
Justin Lee Yeah, it makes sense to a certain extent. I think it would have been better if the rule was that 5^0 were 5 itself, and then 5^1 was (5)*5, which is 25, then 5^2 was (5)*5*5 = 125
Thank you! Now i understood it already haha i will tell this to my math teacher because he said the real answer is not really 1 because you cant raise anything to nothing haha so i did my research and so far this is the best explanation i saw! Very clear 😇
Any base with an exponent divided by the same base with the same exponent will always be 1. That does not mean if the base is zero then the equation becomes 0/0, because it isn't. Let me quote a comment above because he explained this very well. "Plenty of mathematicians use the definition 0^0 := 1. The issue here is that exponentiation has a multitude of definitions. One possible definition for x^n is that you are multiplying x together n times. So the exponent represents an amount of times you multiply something together. This only works for non-negative integers n. But you can extend it to integers or rational numbers by insisting that the laws of exponentiation work. If you want real number or complex exponents, then you have to use a different definition of exponentiation. One involving limits or logarithms. Definitions of exponentiation which are based on repeated multiplication must yield x^0 = 1 for all x (including 0). Definitions of exponentiation which use limits and logarithms leave expressions like 0^x undefined. So mathematicians who fall under the umbrella of discrete mathematics (such as logicians, set theorists, graph theorists, etc. and often algebraists too) are all perfectly fine with 0^0 = 1. It's the only thing that 0^0 could be based on their definition of exponentiation. People who work with continuity, like analysts (and what you do in calculus), often leave exponentiation of 0 undefined because there is no way to make it continuous."
1^0 = 1. But 1^0 + 1^0 = 2? Or 1^0 + 1^0 = 2^0 = 1? Numbers with zero exponents belonged to zero dimentionality and with exponent 1 to one dimention and you cannot add up numbers with zero exponent to make it equal to 2¹. Adding up all numbers with zero dimention will ended up to a point and doesn't make sense adding up 1^0 + 1^0 = 2? 🙏 Thanks
But don't we start with x over 1 and not x over x? 3 isn't 3 over 3. It's 3 over 1. Your equation makes sense. I just don't know how you get from the original number to x over x.
This explanation fails when using a negative base. For example, -1^0 -1^1/-1^1 -1/-1 1. Using his explanation, we get that -1 to the power of 0 is one. But that is incorrect. -1 to the power 0 is -1.
Was searching for mathematical explaination for this ques,clicked on his video he looks very much familiar with johnny sins that makes me check twice that whether or not i am on correct website.
Raising to the 0 power as long as the base is not 0 means that you're not multiplying by anything since there is an invisible 1 that nobody writes because 1 multiplied by that number is the number itself. You can also think of the number dividing by the same number, which is always equal to 1 as long as the number is not zero. 0^0=0/0 is indeterminate. This is an exception since we cannot cancel the 0's because of division by 0. Let's x^3. This means 1*x*x*x. When you go backwards until you reach x^0, you get 1. Raising the negative integer power means how many times you are dividing by that number. Let's say x^-2=1/x^2. This means 1/(x*x). You can think of it as x^3/x^5 using properties of exponents, which is x^(3-5), or by canceling out the x's. All you have left is 1/x^2.
@@justabunga1 you're actually wrong a about 0^0 . x^(a-b) = x^a/x^b only if x≠0 because if you allow x=0 then 0^0 would equal to 0/0 which is not correct in algebra. 0^0 = 1 by convention and by the rule of the empty product (just like 0! = 1) which equals 1. that's why you must add the argument x≠0. Only in analysis like functions and limits 0^0 can be 0,1 or indetermined.
@@pikabuu6315 0^0 is always going to be undefined if you're trying to do computation. By convention (i.e. when doing summation), 0^0 is assumed to be 1 (e.g. finding the sum of y=e^x when x=0). In calculus, we cannot draw the conclusion of 0^0 since it's an indeterminate form.
It's funny how often simple properties of mathematics are overlooked. Thank you for the simple and effective explanation.
I agree, and that you for watching
@@brianmclogan I feel like it still wasn’t explained. So if I’m not dividing exponents, why does any number to the power of zero still equal 1?
not a problem, I think it's important for others to understand why raising to the zero power equals one rather than just taking it for granted
Thank u :)
Your explanation is wrong and it can't be equal to one I have a proof.. I am genius lol just kidding I am not but yes I found how..
Maths isn't about just itself.. Maths is something which is beyond your perception I guess.. Loving maths is good but best when u know it's implications..
Thank you! Instead of just having to remember a rule, now I'll never forget that raising a number to the zero power = 1 because of the LOGIC behind it. The world needs good math teachers like you!
I agree. You are a brilliant teacher!
@@barbarahermannster ? HOW is Linda McCusker a brilliant teacher if he/she isn't the one who was talking in the video?
Now I’ll act like a genius after knowing
First UA-cam channel which tells the reason behind every thing
9 years later and here I am. What an extraordinary teacher.
I'm with the girl on this one. Like her, yes, I understand why the rules of math mean x^0 = 1. But there is no real intuitive explanation here as to why this is so. When she asked for that, you just repeated the rules of math to explain it. I think she understands that x^y/x^y = 1, and that x^y-y = x ^ 0. What she wants t know is how to interpret this in the physical world. Can you give a physical example?
you are very welcome! happy to help
This video was uploaded 8 years ago and I am watching it 8 years later after it was uploaded 😂
Hilarious 😂
Ah yes, the floor is made of floor
Had to write an algorithm in Python using this concept, if any number is raised to the power of zero - this explanation helped me fix some bugs. Thank you Brian from 9 years ago, appreciate it
I just started learning python yesterday. I already know some web development, I have learned in the past CSS, SASS, JavaScript, jQuary, how to use npm, git, grunt and webpack, and I have also learned mySQL, now I decided to learn python so that I can hopefully start understanding how backend works better and create web applications in the future. Front end is kind of annoying actually, I suck as CSS, so I want to become a back end developer. I however haven't really decided what I want to do yet, I just learn things that may be useful in the future, I was also interested in hacking so I learned some basic stuff about networking but I haven't yet learned anything about hacking because I didn't have the time. I also had studied logical gates once and made a calculator that could add and substract, I was planning to make a full ALU but gave up eventually because I had other stuff to do.
Thank you! New teacher here......didn't know how to explain this to students....I thought the proof was much longer. THANK YOU!!
well writing a proof would be, this is just an example to help understand
very professional .i love it .thanks Sir.
you are very welcome!
your welcome, glad I could help
It looks very simple, I searched for this because I was solving non-exact differential equations and I often get this term. Thanks!
To help explain the person question some more.
x^5/x^2 is essentially x*x*x*x*x/x*x
We know that if a the same thing in the numerator is in the denominator then it cancels out.
This would leave you with 2 x’s canceled at the bottom and top. But that leaves 3 x’s on the top.
So, You had 5 x’sat the top and 2 x’s at the bottom but after canceling those x’s out you’re left with 3 x’s.
That’s why you have to subtract exponents.
Tbh I’m only explaining this so it can stick in my head better.
Finally, a video that actually EXPLAINS how X to the power of zero is 1. All the other videos say that they will EXPLAIN but they don’t explain anything they just say that X over X equals 1. This guy ACTUALLY explains it with the a - b analogy.
Love this, thank you so much. Is there a way you can explain it to someone who isn't familiar with the rules of exponents? Thank you so much
Simple and elegant ! Thanks Brian. Keep going !
think about it this way 1*0=0, 1/0 = ? There fore ?*0 = 1 but anything times zero equals 0 and 0 does not equal one. That is why 1/0 is undefined.
Very well explained.Thank you very much.
Is there any way to explain this without the dividing exponents rule? For me explaining a rule of math "x^0=1" using another rule of math does not help me actually understand it. Still just sounds like your saying it makes sense bc it's the rule.
This is a very intuitive reply. If an exponent is simply the number of times the base is a factor...well by definition, a factor has to be multiplied by something. So 5 to the first power means 5 as a factor once... But if it is a factor... It has to be multiplied by another factor. That other factor is the implied 1. So 1 x 5 = 5. So 5^0 Means there is a factor, but not any 5. So then you just have the implied 1 as a factor. And since 1 by itself has no other factors, only 1 can stand alone. The rule mentioned doesn't really explain why a number to the 0 power is one. It's just the unsimplified form...
So the rule of Zero Exponent is Devide the Number by itself?
Good explanations and easy to understand... Thanks
This has bugged me for close to thirty years. Thank you!
you are very welcome Jon!
X^a=X^a
X^a+0=X^a( Because of
Additive Identity property of real numbers)
X^a *X^0=X^a
X^0=X^a÷X^a
X^0=1
Didn't get the third step
@@jayaramj9630
X^(a+b)=(X^a)*(X^b)
This makes perfect sense . Thank you for the video.
It's very interesting to hear everyone explain this. Many people are able to make the connections on why it's intuitively 1 (like what you've done here) as well as if you look at (for example) 2^4 = 16, 2^3 = 8, 2^2 = 4, 2^1= 2, 2^0=1 and how you're dividing by 2 each step you go, but I guess it just seems bizarre when you think about what exponent is and you think '5 time itself zero times equals...1'
Thanks for offering up a different explanation than normal though!
Excellent simple explanation using deductive reasoning.
This helped me understand this alot better. I know the rule ,but I didn't understand why the rule works. Our teacher just told us what rule is instead of why it's that way. Thank you.
you are very welcome! happy to be able to help
I love how a simple rule causes confusion for many young mathematicians. After watching this video and understanding it, I feel quite smart now lol
I don't speak English, but I understood the mathemathic problem. Thanks!
Just follow the rule thats why, dont try to understand.
I get the rule but like if an exponent is the base times the exponent so X times 0 it should be 0, what bugs me is if you are using math to as an example backup a theory in idk lets say theorical physics and you use this rule to come up with matter out of nowhere it just wouldn't make much sense under some situations
Now this makes so much more sense! Thank you good sir!!
I have always found the exponent rules to be intriguing. Intuitively, if someone were to ask me what is 5^0, I would just tell them 5; knowing that an exponent tells you how many times you should multiply a value/variable/expression by itself, if you asked me what 5^0 was, I would tell you to multiply 5 by itself 0 times, meaning don't multiply at all, and you are left with 5. I'm not sure how to get around that. :(
Shean Crane Not multiplying at all basically means we get 1 as whenever we multiply any number n times we start off with 1 and then multiple n times hence if we don’t multiply at all, we’re basically left with just 1.
The 0 power means that you're not multiplying by anything or you're dividing the number by the same number itself, which is always to equal to 1 as long as the number is not zero. When I mean you're not multiplying by anything, it's saying that there is an invisible 1 that nobody writes because 1 multiplied by any number is number itself. Let's say 5^3=1*5*5*5. As you go backwards by canceling out the 5's until you reach 5^0, you will get 1.
@@justabunga1 is the 1 multiplied in your example because there is always an invisible 1 under every number? then when we multiply we must multiply it by it’s reciprocal being 1/1 which equals 1 i.e. (5/1)^3 -> 5^3 = 5*5*5*1/1?
@@AnthonyTurcios no, the "1" that is being multiplied by any number just leaves that number unchanged. That is called a multiplicative identity. Therefore, any non-zero number raised to the power of 0 is always equal to 1. Take for example, 2^4=2*2*2*2=16. If we count down the powers of exponents until 0, then the problem arises. That's why there is an invisible 1 there. 2^4 is supposed to be the same as 1*2*2*2*2 if you notice that there is a 1 being multiplied from there and then 2 four times. That's why no one writes the 1 there.
@@justabunga1 I see, I understand the explanation, just I'm a little more confused to as with the why of the explanation.
Thank you, Glad I found your channel. Helping my son with this stuff. It's been 40 years since I sat in a math class.
so happy to be able to help, bless you having to go back and work to remember this stuff
you explain these things very well
Positive exponents are about repeated multiplication while negative exponents are about repeated division. That's it and it's enough. But some twisted mathematicians had to make it weird. The x^0=1 is not needed and it goes against the very definition of exponent which clearly states "The exponent of a number says how many times to use the number in a multiplication". So, if the power is 0 what should be the result based on the definition?
Great explaination! You make it easy to understand!
short make sense and simple, thank u
Wow sir you are a brilliant teacher it was looking so difficult but you made it very easy thank you so much......👍
Marvellous .. good job 👏👏
Keep going 👍
Thanks to remove my confusion
You explained it perfectly.
It’s actually any non-zero number raised to 0 power is always equal to 1. If it’s 0^0, the answer is indeterminate. When you deal with limits using calculus i.e. l’Hopital’s rule, you will have to do more work since it’s one of the 7 indeterminate forms.
NO!
@@seroujghazarian6343 0^0=1 by convention only when you work with power series like y=e^x or y=1/(1-x) when you do the summation.
@@justabunga1 card({}^{})
Very good 👍🙂
this clears up the argument in my class, if the power of 0 equals 1 or the base number.
I Have Seen Enough
Now I Am Satisfied.
Oh wow, I instantly understood it! Thanks!
I’m in Calc 2 right now and have never really known why this is true, only that it is. When you think of it that way, it really is quite simple. Is this also why 0^0 is indeterminate? Because it would simply simplify to 0^1/0^1 =0/0 = undefined?
Thank you sir❤️
I get everything that was said, but why do we have to divide exponents? This might be a stupid question but really, I am so curious.
After my math teacher trying to explain in, I get it now. Thankyou.
happy to help
Thanks! We took this lesson today and our teacher didn't tell us the reason why it is always 1. And when we asked her she said search it up.
haha well there I am!
Whn y is not equal to zero
@@shraddhasharma7409 magic
Is x^0 actualy defined as x/x
because right next to it is x^-1 is x/x/x so its just a continuation down the number line of exponents?
but why would you divide i don't get it O_O
very good and easy explanation!
you are very welcome!
Well explained
Good explanation . I understood
thank you sir this was a helpfull video
you are very welcome!
I get the reason behind the explanation. I think it's the order of logic that makes this confusing still to me and others. It sounds like dividing exponents must be known before one can understand the one equation in understanding exponents (e.g. before one can learn what '9' is one must study division). It was explained best by a prior comment: (essentially) mathematicians did not have a definition for x^0, so to make sense of the concept, they used principles of other formulas such as the exchangeable properties in addition and the formula for division.
very well put, agree
That's a good explanation of why this is so. When learning math concepts there is a large bit of acceptance that a student needs to be willing to give, the same is true with language use and learning, and Id say with most thing we do in life. If a student wants to know why a concept is than they need to look to the proofs for that concept and also I guess understand that math is both art and science and used in applications but for the science part it is trusted that if a concept is shown to be true than that is the accepted reality for the moment and people just go with that. As a real application of this concept, computers use this idea in constructing a binary number and this is an example of an application of this accepted concept. I may be right, I may be wrong, but that is my comment on this at the moment.
this helped me thanks man
you are very welcome!
I suppose x^0=1 is simply the current mathematical convention. It just can't make sense of it.
So what it they both didn't have the same exponents? This rule wouldn't apply then right ?
X^1/x^2 = X^1-2 = X^1 = X so no without the same exponent they wouldnt come down to 0
Very good and helpful
happy to help
That was a good explanation, don't listen to hate brother. Happy holidays!
cheers appreciate it
I will act like a genius after knowing this thank mr.brian
Question: if x to the power of 2 = x times x
and x to the power of 1 = x
then what is the actual equation for x to the power of 0?
Actually, the rules says X^n = Xx.......xX ONLY if the exponent n is equal or superior to 2...
x to the power 0 = 1
Anna Pritchard If you notice at each stage we divide by x so x^0=x/x=1
Anna Pritchard there’s an invisible 1 that nobody writes because of the multiplicative identity since 1 times any number is any number. From your example, x^2=1*x*x. Then, x^1=1*x. What is x^0? The answer is 1 as long as x is not 0 since 0^0 is indeterminate. The 0 power means that you’re not multiplying x by anything. I know it sounds like it doesn’t sense, but you will get the logic of how it works.
*Then 0 raised to 0 is Zero why* ...*🦧😅🤣
You are god making matter out of nowhere c:
those kids coughing an awful lot. who got that cart?
You didn’t mention exceptions. A negative number without parentheses raised to zero equals -1, and 0^0 has no meaning.
correct, thanks
Thank you.
I don't know what that means, but you are welcome? haha
im here because cha eun woo solved a problem with this. I never listened to my math teacher to know about this rule
x/x = 1(any number divided by itself is 1), what if x=0? 0/0 = 1? Maybe a number at the power of "0" should be undefined or "0"
+binixx yes based on euler's definition
This should be any non-zero number divided any non-zero number is always 1. 0/0 and 0^0 are both indeterminate.
And here my teacher "it is written in the book na so just memorize it
Don't be oversmart
I am literally a 30 y old boomer and never understood why this was the case, thanks for making me a little bit less ignorant bro :')
Times are changing people. My teachers have finally noticed that UA-cam has taught more stuff than anyone or anything else. XDD
This did not prove that any number to the power of zero equals 1, all that was taught here is that it's a rule
correct, I did not use a proof
multiplying no numbers at all should give the multiplicative identity. Now, what's the multiplicative identity? Well, it's the only number which can be multiplied by any other number without changing that other number. In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
@@brianmclogan Why your student said "No, it doesn't make sense. I see how you did it."
@@SixmillyJ That's correct. Raising to the 0 power means that you're not multiplying any numbers. It's the invisible 1 that nobody writes because of the multiplicative identity, which says any number multiplied by 1 is the number itself. You can also think of it as dividing the number by the same number, which is always equal to 1 as long as that number is not 0. For example, 4^6=1*4*4*4*4*4*4. When you cancel out the 4's until you reach 4^0, you get 1.
Ah Ok my confusion was because multiplying by zero equals zero, but this is different...because of that exponent division rule. Thanks!
you are very welcome!
I think that human understanding of mathematics is incomplete.
Almost, it’s just the extension of the rules to zero and negatives. But this is the best explanation by far
Amazing sir!
I think it's still doesn't make much sense. Not blaming the professor, but the rule itself. 5/5, 10/10 or a number divided by itself is always one obviously, but 5 by itself is 5, or a number by itself is just that number. Why would it be 1 if you have it to the exponent zero, but there is no division?
There's another way that you can think of since that is correct by the way. The 0 power means that you're not multiplying by the number itself. It's the 1 that is being multiplied since it's not written and nobody writes that because of the multiplicative identity, which says that 1 times any number is the number itself. Let's say 9^5=1*9*9*9*9*9. When you cancel out the 9's until you reach 9^0, all you have left is 1.
Justin Lee Yeah, it makes sense to a certain extent. I think it would have been better if the rule was that 5^0 were 5 itself, and then 5^1 was (5)*5, which is 25, then 5^2 was (5)*5*5 = 125
Thank you! Now i understood it already haha i will tell this to my math teacher because he said the real answer is not really 1 because you cant raise anything to nothing haha so i did my research and so far this is the best explanation i saw! Very clear 😇
+Angel Ma you are welcome, this video is an explanation of why any number raised to the zero is 1 but not a proof
So you're saying that any number divided by itself gives 1 then what happens if 0 divided by 0.
Any base with an exponent divided by the same base with the same exponent will always be 1. That does not mean if the base is zero then the equation becomes 0/0, because it isn't. Let me quote a comment above because he explained this very well.
"Plenty of mathematicians use the definition 0^0 := 1.
The issue here is that exponentiation has a multitude of definitions.
One possible definition for x^n is that you are multiplying x together n times. So the exponent represents an amount of times you multiply something together. This only works for non-negative integers n. But you can extend it to integers or rational numbers by insisting that the laws of exponentiation work.
If you want real number or complex exponents, then you have to use a different definition of exponentiation. One involving limits or logarithms.
Definitions of exponentiation which are based on repeated multiplication must yield x^0 = 1 for all x (including 0). Definitions of exponentiation which use limits and logarithms leave expressions like 0^x undefined.
So mathematicians who fall under the umbrella of discrete mathematics (such as logicians, set theorists, graph theorists, etc. and often algebraists too) are all perfectly fine with 0^0 = 1. It's the only thing that 0^0 could be based on their definition of exponentiation. People who work with continuity, like analysts (and what you do in calculus), often leave exponentiation of 0 undefined because there is no way to make it continuous."
Sappy 0^0=1 by convention only when you do power series. Otherwise, in general, 0^0 is indeterminate.
1^0 = 1. But 1^0 + 1^0 = 2? Or 1^0 + 1^0 = 2^0 = 1? Numbers with zero exponents belonged to zero dimentionality and with exponent 1 to one dimention and you cannot add up numbers with zero exponent to make it equal to 2¹. Adding up all numbers with zero dimention will ended up to a point and doesn't make sense adding up 1^0 + 1^0 = 2? 🙏 Thanks
But don't we start with x over 1 and not x over x? 3 isn't 3 over 3. It's 3 over 1. Your equation makes sense. I just don't know how you get from the original number to x over x.
Plot twist: x=0 therefore, x^3/x^3 = 0/0 which is undefined
which we discuss in my calculus class, but not algebra 1
0^0 is the only case where x/x is not equal to x^0.
Why? Because 0/0 can also be 0²/0¹=0¹=0
Serouj Ghazarian that’s right. Both 0/0 and 0^0 can’t be assigned to a single value. That’s why it’s indeterminate.
HowToDrinkBleachAndNotDie 0^0 is indeterminate just like 0/0.
Hello sir,,, agar 2 ki power 4time 2 ho aur uski power 0 ho to kya answer milega ?
Mean 2^²^²^²^² ka whole power 0 equal what
Aman Srivastava It would be the resultant number raised to zero which will still give the value 1
you mean --- the number divide it self equal == 1 --- right my pro
This explanation fails when using a negative base.
For example, -1^0 -1^1/-1^1 -1/-1 1.
Using his explanation, we get that -1 to the power of 0 is one. But that is incorrect. -1 to the power 0 is -1.
-1 to the power of 0 is 1, not -1. I suspect you typed it in to a calculator incorrectly. You want (-1)^0, not -(1^0).
EvaUnit02 You’re right! I noticed just after posing the comment !
The 0th degree of an exponent defines the base unit. Not an operation. A definition.
Was searching for mathematical explaination for this ques,clicked on his video he looks very much familiar with johnny sins that makes me check twice that whether or not i am on correct website.
thank you.
0^(0) = undefined
How about just putting your arguments together in a single proof like this: x^0 = x^(1-1) = x^1 / x^1 = 1
yes was just an impromptu video I made while teaching
so why isnt x to the zero power zero and x to the negative 1 power divided by itself once to make it 1? I still dont understand
Raising to the 0 power as long as the base is not 0 means that you're not multiplying by anything since there is an invisible 1 that nobody writes because 1 multiplied by that number is the number itself. You can also think of the number dividing by the same number, which is always equal to 1 as long as the number is not zero. 0^0=0/0 is indeterminate. This is an exception since we cannot cancel the 0's because of division by 0. Let's x^3. This means 1*x*x*x. When you go backwards until you reach x^0, you get 1. Raising the negative integer power means how many times you are dividing by that number. Let's say x^-2=1/x^2. This means 1/(x*x). You can think of it as x^3/x^5 using properties of exponents, which is x^(3-5), or by canceling out the x's. All you have left is 1/x^2.
@@justabunga1 you're actually wrong a about 0^0 . x^(a-b) = x^a/x^b only if x≠0 because if you allow x=0 then 0^0 would equal to 0/0 which is not correct in algebra. 0^0 = 1 by convention and by the rule of the empty product (just like 0! = 1) which equals 1. that's why you must add the argument x≠0. Only in analysis like functions and limits 0^0 can be 0,1 or indetermined.
@@pikabuu6315 0^0 is always going to be undefined if you're trying to do computation. By convention (i.e. when doing summation), 0^0 is assumed to be 1 (e.g. finding the sum of y=e^x when x=0). In calculus, we cannot draw the conclusion of 0^0 since it's an indeterminate form.
Nice!
thanks!