Very very odd. Some implicit rules need to be added: eg the indices m and n can also be interchangeable so that m's 'value' can equal n's and/or n can=m or in other words we can have the same 'values' for m and n, apparently nothing stopping us doing that in Maths, or, rather, a^m and a^n don't have to be mutually exclusive for Rule +1 to 'work' - any indices, the same or different will work, obviously. ... ..However, for the sake of providing absolute clarity later we do need to be explicit: ro rule - or Law #1 can be be restated as a^m x a^n = (or can equal) m and n being the same value if so desired. All very superflous and even tautological I know, at this 'stage' of Rule / Law #1 in isolation but quite important later. OK, so far so good. Right, that then covers us for Rule number 2 and that then leads naturally enough to a^0=1. The rules are not 'transferable' in isolation from each other - ie Rule 3 cannot be deduced from Rule 1 in isolation, as the Laws are shown in your presentation. . Or in other words, a^0 =1 only when applied to Rule 1 (modified or augmented as above by me) + Rule 2 combined, or, to labour the point, a^0=1 only applies to division when m and n are the same value or, if you will, it won't 'work' if the integers of the indices are different. . But of course in your presentation of the rules does not include that stipulation. I know what I am saying above is very circular from the view point of a Mathematician but not from the view point of a lay person - these things need to be spelled out very specifically. Even when the process is spelled out, it looks like 'zero' is some kind of weird quasi 'integer'..... 3 or 6 or anything x0=1??? Huh? And in the final analysis, in my way of thinking, the above is a 'justification' of at least one of Godel's theorems - that what is a true statement in Maths can't neccesarily be proved. But Maths tries to keep a lid on that by saying because it is 'By Definition' (such as x^0 =1) it does not NEED to be proved. Can it be proved? 'Come on now, you're just being deliberately obscurant and silly!' says the Mathematician in exasperation. If pushed, that Mathematician may finally say Well, no, we can't 'prove it' - we can 'justify' it using our own internal logic and there are a number of ways of doing so and that is the best we can offer Like it or lump it'.
I accept your point that x to the power of x approaches 1 in the limit as x approaches 0. However, 0 to the power of zero is undefined as 0 to the power of zero using the law of indices could be re-expressed as 0 to the power of one divided by zero to the power of one and any number divided by zero to the power of one is undefined because zero to the power of 1 is zero.
For the eg 2^3 x 3^-5, could you do 2x3 which is 6, then for the powers do 3+(-5) which is -2. So the answer would be 6^-2 which is 1/6^2 or 1/36. But the actual answer is 8/243. So what have I done wrong?
Probably a little late, but index laws only apply when the base is the same. Can be shown with a simple example 2^2 x 1^3 = 4 x 1 = 4 If what you said was true it would be 2^2 x 1^3 = 2^5 = 32
Hi Eddie. Just wondering what would happen if there is a variable? My question is 5x^-2= My answer was 1/5x^2 but the answer sheet says 5/x^2. I'm a bit confused about why you would move the 5 from the denominator to the numerator? PLEASE HELP!!! THANK YOU
wait arent you guy that from the tv? (edited) I getting to unstated it but still confused. when i saw a student gave the paper to the teacher, i know that feeling. lAtE cRaD
Can I ask u one question the question is evaluate 1.-3/5 raise the power-4 ×-2/5 raise the power 2 , so this is ur answer I want answer only from this teacher, I want to see how perfect he is in maths
Given: (-3/5)^(-4) * (-2/5)^2 Because the -4 is negative, we can flip the fraction and clear the exponent's negative sign. Because (1/x)^n = x^(-n). (-3/5)^(-4) = (-5/3)^4 Because this is an even power, this means that a negative base will return a positive answer. Squaring a negative sign will remove it, since (-1)*(-1) = +1. You do need to indicate this properly, such that the negative is inside the parenthesis, because "A minus ain't squared, unless it's been snared". Implement our simplification thus far: (5/3)^4 * (-2/5)^2 Do the same with the squaring of (-2/5): (-2/5)^2 = (2/5)^2 Reconstruct: (5/3)^4 * (2/5)^2 Group the 5's: 5^4 * (1/5)^2 * (1/3)^4 * 2^2 Rewrite 5^4 as 5^2 * 5^2, and cancel the 5^2: 5^2 * (1/3)^4 * 2^2 Fill in with what we know, from multiplication tables: 5^2 = 25 3^2 = 81 2^2 = 4 And our answer is: 100/81
i would like to meet Mr Woo in real life
damm need him as my math teacher
Props to the kid that came late.
Wow, you are so passionate about teaching. Thankyou for your service to humanity !
@French Baguette he doesn't exist in humanity's world, humanity is living in his world.
@@twelvoe4205good to me to on on my ok
Thank you! I have a test tomorrow and my teacher is like a text book... so hard to learn! Thanks for making it easy!
It’s just like all Egyptian teachers
Same
im just curious if that boy found this calculator or not
rumour has it that 6 years later, pashir is still searching for his lost calculator
@@gretah70 at least he now knows how to open a door !!!
Its been said that pashir's lost calculator was the cause of the worldwide pandemic
you make it so simple! Thanks so much!
you sir, just saved my math grade. night before test and i now know all about negative indices.
To think that I'm watching this 10 years after it was posted is mind blowing
Thanks a lot, Eddie sir! You remind me of my teacher at school! Very enthusiastic and energetic and also very kind! Thanks a lot!
You can say Mr. Woo is teaching because the students are LEARNING!!!!
Bro they be experiencing the best maths class 😂
i was struggling so much
Damn even the small things matter. Instead of writing it as 6/24/14, he wrote it as 24/6/14. Respect.
what? thats cuz hes australian mate, nothing special
obviously it’s australia how else would he write it
How can this video have any NEGATIVE likes? How can any video that he does have any negative likes? Keep up the good work.
Don’t you mean dislikes? Johnathan?
May god bless u💦💝...I know Negative indices well now
thanks eddie i learned i lot this will help my kid who is in school right now
LEGEND
Dman, u helped me in my exam, THX U
If negative indices are on the denominator, does it go to the numerator?
yes they do
Eg 1/2^-3 = 2/1^3
@Uni YI
an example of the descripted text
@@akshatsingh7286 False! 1/2^-3 = 1/(1/2^3)=2^3
You are the coolest teacher
best maths teacher out here
I’m loving this series. You’re terrific!
Great video
Better then my fishy teacher ngl
do one on negative indices for summations and shifting the index please
Thank you helpful sir
Very very odd. Some implicit rules need to be added: eg the indices m and n can also be interchangeable so that m's 'value' can equal n's and/or n can=m or in other words we can have the same 'values' for m and n, apparently nothing stopping us doing that in Maths, or, rather, a^m and a^n don't have to be mutually exclusive for Rule +1 to 'work' - any indices, the same or different will work, obviously. ... ..However, for the sake of providing absolute clarity later we do need to be explicit: ro rule - or Law #1 can be be restated as a^m x a^n = (or can equal) m and n being the same value if so desired. All very superflous and even tautological I know, at this 'stage' of Rule / Law #1 in isolation but quite important later.
OK, so far so good. Right, that then covers us for Rule number 2 and that then leads naturally enough to a^0=1. The rules are not 'transferable' in isolation from each other - ie Rule 3 cannot be deduced from Rule 1 in isolation, as the Laws are shown in your presentation. . Or in other words, a^0 =1 only when applied to Rule 1 (modified or augmented as above by me) + Rule 2 combined, or, to labour the point, a^0=1 only applies to division when m and n are the same value or, if you will, it won't 'work' if the integers of the indices are different. . But of course in your presentation of the rules does not include that stipulation.
I know what I am saying above is very circular from the view point of a Mathematician but not from the view point of a lay person - these things need to be spelled out very specifically. Even when the process is spelled out, it looks like 'zero' is some kind of weird quasi 'integer'..... 3 or 6 or anything x0=1??? Huh?
And in the final analysis, in my way of thinking, the above is a 'justification' of at least one of Godel's theorems - that what is a true statement in Maths can't neccesarily be proved. But Maths tries to keep a lid on that by saying because it is 'By Definition' (such as x^0 =1) it does not NEED to be proved. Can it be proved? 'Come on now, you're just being deliberately obscurant and silly!' says the Mathematician in exasperation. If pushed, that Mathematician may finally say Well, no, we can't 'prove it' - we can 'justify' it using our own internal logic and there are a number of ways of doing so and that is the best we can offer Like it or lump it'.
Thank you so much I'm studying for exams and I didn't understand this at all I completely understand it now thanks to this video !!
legend
Ur students are lucky
I accept your point that x to the power of x approaches 1 in the limit as x approaches 0. However, 0 to the power of zero is undefined as 0 to the power of zero using the law of indices could be re-expressed as 0 to the power of one divided by zero to the power of one and any number divided by zero to the power of one is undefined because zero to the power of 1 is zero.
That poor guy, did he find his calculator, the feels are flowing for him, he mus tbe pretty negative right now ;)
That guy crossed the line by entering the class
i wish my teacher was this good at explaining smh
Are you Aussie? I am. I can sorta hear it in your voice awesome video btw
i am basically looking at things higher than my grade
For the eg 2^3 x 3^-5, could you do 2x3 which is 6, then for the powers do 3+(-5) which is -2. So the answer would be 6^-2 which is 1/6^2 or 1/36. But the actual answer is 8/243. So what have I done wrong?
Probably a little late, but index laws only apply when the base is the same. Can be shown with a simple example
2^2 x 1^3 = 4 x 1 = 4
If what you said was true it would be
2^2 x 1^3 = 2^5 = 32
Ur good
Guys, what year level is this?
Hi Eddie. Just wondering what would happen if there is a variable? My question is 5x^-2=
My answer was 1/5x^2 but the answer sheet says 5/x^2. I'm a bit confused about why you would move the 5 from the denominator to the numerator? PLEASE HELP!!! THANK YOU
This is because 5 is the coefficient of x^-2. The only thing being raised to the power of -2 is x. You can view it like this: (5)(1/x^2)
❤😅😮
,,,,,,,
i wish you were my math teacher
wait arent you guy that from the tv?
(edited)
I getting to unstated it but still confused.
when i saw a student gave the paper to the teacher, i know that feeling.
lAtE cRaD
quick question to anyone
how do you multiply a negative indice by a positive indice, is it like when you add a positive to a negative?
wish you were my teacher!
Can I ask u one question the question is evaluate 1.-3/5 raise the power-4 ×-2/5 raise the power 2 , so this is ur answer I want answer only from this teacher, I want to see how perfect he is in maths
Given:
(-3/5)^(-4) * (-2/5)^2
Because the -4 is negative, we can flip the fraction and clear the exponent's negative sign. Because (1/x)^n = x^(-n).
(-3/5)^(-4) = (-5/3)^4
Because this is an even power, this means that a negative base will return a positive answer. Squaring a negative sign will remove it, since (-1)*(-1) = +1. You do need to indicate this properly, such that the negative is inside the parenthesis, because "A minus ain't squared, unless it's been snared".
Implement our simplification thus far:
(5/3)^4 * (-2/5)^2
Do the same with the squaring of (-2/5):
(-2/5)^2 = (2/5)^2
Reconstruct:
(5/3)^4 * (2/5)^2
Group the 5's:
5^4 * (1/5)^2 * (1/3)^4 * 2^2
Rewrite 5^4 as 5^2 * 5^2, and cancel the 5^2:
5^2 * (1/3)^4 * 2^2
Fill in with what we know, from multiplication tables:
5^2 = 25
3^2 = 81
2^2 = 4
And our answer is:
100/81
is this class in the UK ??
Sydney, Australia
What is this subject?
Geography
i have an exam on this tomorrow hope to god i pass thank you eddie for the education
So grateful for the questioner at 5:54! The answer to that was the key to it!
can you tell me what he was asking? im not english, so its hard to just listen. Thanks
Hang on, I don't recall asking
he kinda look like rice gum lol
XD
op