Rules of Exponents (Multiplying, Dividing, Roots) Algebra with JusticeTheTutor

[@Fan-qu8qy]

This might be 6th grade math but it’s helpful to many of all ages.

[@e_pi_i_is_-1]

Pls don't differentiate math into grades here. If u go behind the proofs then it becomes much better

[@eruptrl8893]

@@e_pi_i_is_-1 I don’t get what you mean

[@gwho.park5]

Bro i haven’t even learned this in school and I’m in 8th grade. I go to tutor tho for algebra 1 but my school is so slow

[@lowellhawk1039]

@@gwho.park5 No that is normal I learned this in 8th grade advanced math and that school is one of the best in my state i think he was just exaggerating

[@lilycorne9503]

It’s late

[@gonzalotapia1250]

Please note the difference between the 3rd and 5th cases. The parenthesis makes all the difference.

[@dhdusidjdjso]

On so many math videos people always say the video is wrong when it’s actually them thinking the 3rd and 5th cases are the same

[@needshelpwithprocrastination]

Can you pls explain I don’t really understand

[@dhdusidjdjso]

@@needshelpwithprocrastination When it is (a^b)^c, you can multiply the exponents, so you get a^bc. When it is a^b^c, you have to exponentiate b^c and then a to that, so you get a^(b^c)

[@needshelpwithprocrastination]

@@dhdusidjdjso ohhhhhhhh

[@maxcool6946]

Could’ve used this 6 years ago thanks man👍

[@aki.1313]

Doing this in 9th grade and never really got to understand, thanks this helps!

[@michaelnorumlawyers]

Who dis? PMGS ..yes / no?😅

[@thegreatweeb9000]

Same

[@tejasvvisarvasiddi4666]

If you are unable to understand this kiddo problem even in class 9 then you are definitely a Dumbo. 😂

[@avyankumarsrivastava2905]

Brother we did this in 6th and understood

[@aki.1313]

@@avyankumarsrivastava2905 Cool! I was online during covid so we didn't get to learn a lot of material, thanks for your input though! Glad you were able to learn this earlier and not struggle like me :)

[@Kusum_Patra2812]

X ^0 =1, X ^ -m = 1 / X ^m

[@Vanduo610]

X^y + Y^x?

[@superredcar7641]

Thanks Mam ....it is very useful and basic ..... Very good 👍😊😊

[@MrAlexChoyce]

When stacking exponents you use exponents to figure out what number to use for the final number (this case is used a ton in tetration)

[@vora300]

Second year of computer engineering and I sometimes forget thinks like this.

[@yahiamohamed1675]

Bruh that helped more than a 4 mins video

[@thegreatweeb9000]

Same

[@sureshl9534]

Super thank you

[@Rabbit-the-One]

Nicely put

[@Momaka221]

x to the power 16 .

[@coden2974]

yeah ikr

[@leasol8659]

🎉❤

[@dayster3693]

What is the last number answer

[@Dineazly]

The last one is technically incorrect. If it has more than 1 exponent, it has to multiply it Etc. (x^4)^2 = x^(4×2) Therefore, the answer must be x^8 But this answer will be correct if you mean x^(4^2)

[@the_lava_wielder6996]

That notation means x^(4^2) There would be no use defining it as being (x^4)^2 because yes, you could just multiply it

[@jaypark7774]

a1^a2^a3...^a_n is defined from top to bottom, so in this case it is a^(b^c)

[@ARTERRRRR]

I swear none of that was English

[@_____JUNPark_____]

Note: √(x^2) is NOT (√x)^2 Because x can be negative, And (x^2) makes it positive. => √(x^2) = |x|

[@YeahMathIsBoring]

True！

[@GauravGamer9]

Explain bro don't add music

[@shahriarmahi17]

(2)

[@Anonymous-hv2zc]

what needs explaining?

[@animethighss69]

@@Anonymous-hv2zc fr

[@lumina_]

it's very self explanatory lmao

[@Slash4608]

What's there to explain?

[@saravanarajeswaran2626]

to be honest there's no need to memorise, just think for a second, if you have x^5, this means you about multiple x by itself 5 times, so x.x.x.x.x and multiplying by x^6 which six x you gonna end up multiplying by x by itself 9 times, there's no way it is hard to understand this rules😭😭😭

[@isavenewspapers8890]

Six plus five is eleven.

[@saravanarajeswaran2626]

@@isavenewspapers8890 dang bro my bad

[@Blessingsuponyou]

After failing Algebra I look at this and some of these operations look logical now as in I spent too much effort, or simply not enough and my brain became disinterested You make it look east

[@ZeeroTwoNone]

My memory literally throws everything thing I learned last year so this is a sorta big help.

[@keatodiet]

You have to practice.

[@keatodiet]

Consistently.

[@tylerdoesdumbstuff]

Idk why I'm getting this in my recommendations, i already know this...

[@rahulisgreat4911]

Thank you

[@UdayKumar-yi1ff]

thanks sir

[@ManasaPodeti25-mf4fy]

How bro pls more video's

[@SHAHRIArFAHImVipPersoN]

thanks a lot of very very much,, for helped us💓💓❤️❤️❤️❤️

[@shaziarahman331]

Bro I have been learning in school this chapter for 1 years and now I totally get this after the video

[@djsistersyoutube]

when do we learn this actually? im turning 5th grade btw.

[@apenas_tarso]

In 15 secomds you explained better than my teacher

[@largestbrain]

No he didn’t. this is what you’re taught in school, you just didn’t pay attention as well as you watch videos on KZbin

[@basilabuse]

@@largestbraingo lose your raincells

[@largestbrain]

@@basilabuse they’re called braincells. Go pay attention in school

[@RobeleJem]

Pls in addition and subtraction

[@bj_weeelkss]

X doesn't exist in the 1st(^) , in any case you need to write just X

[@lizzybach4254]

x^1 = x. They mean the same thing and can be interchanged.

[@Blessingsuponyou]

I still remember some basics Inverse of division is multiplication Pemdas Associate Commutative Foil

[@Nbrother1234]

x^4^2 = x^(4^2)

[@rikun-31415]

x^1=x

[@davidbalog1014]

Last is 4 to the power of 8

[@-jason1912]

There is a difference between (x^4)² and x^4², you know

[@Movie_edits_]

I learned this in 8th grade I’m 8th grade rn

[@leemahsmith2566]

Very hepful

[@lunalostmotivationnotverif4897]

I’m 9 and guesses some algebra right on quizzes

[@sadge824]

So cool omg1!1!1

[@tejasvvisarvasiddi4666]

I am in 4th standard from BHARAT,INDIA and you people look like dumb learning this in 9 th standard

[@FrancismcKampamba]

I like it .❤❤❤it's easy

[@astro_cat030]

Tysm

[@ZainabAli53936]

Last one answer will be 4^16

[@isavenewspapers8890]

Assuming x = 4.

[@idlesquadron7283]

x^4^2 = x^16 right? sorry i'm confused what you said there

[@ermiasberhanugebreselassie1618]

4 the power of 2, that means 4× 4 and the result is 16

[@Edward_Cullen_108]

Thanks 🥹💙

[@leasol8659]

Iam not really that good at mathematics for me it's hard, so in no.5 why though the answer is ×16, I really wanted to learn math so why is that the answer of ×42 is ×16 did you multiply or divide it or plus minus? Plz let me know ❤

[@hardcorelegend7285]

He did power that means that he times 4 2 timed so it's like this 4×4 cuz it said times 4 twice cuz of the little number beside 4 if you wanna know more about thet write "power explained" you usually learn that before exponents tho

[@isavenewspapers8890]

The 2 is an exponent on the 4. You can see that the 2 is raised slightly higher than the 4.

[@AbbChess]

bro, what the hell, the 3rd one is wrong. The exponent outside of the parenthesis applies to the value of x and the exponent inside the parenthesis

[@FuturePast2019]

Great "trick" no light on fingers. Hint for people from India

[@edvinas5555]

How about x²+x³ Or can that only be done with the value of x?

[@amberdavis5311]

Pretty sure it's just how you wrote it. That's the simplest form since the exponents are different. That is what wikiHow says anyway.

[@amberdavis5311]

How were you able to write an exponent? You got some fancy keyboard?

[@isavenewspapers8890]

We can't simplify this into an expression with only one x. However, we can do other things. The expression x^2 + x^3 is known as a polynomial, or an expression with nothing but addition, subtraction, multiplication, and positive-integer powers of variables. This definition is kinda complicated, so don't worry if it's hard to understand at first. x^2 and x^3 are the terms of the polynomial. In other words, they are the things being added together. This is where the word "polynomial" comes from; it is a combination of the Greek "poly", meaning "many", and the Latin "nomen", meaning "name". So "polynomial" means "many-named"; this refers to how a polynomial contains one or more terms. Our polynomial has two terms, so it is called a binomial. (Here, "bi" means "two", like in "bicycle".) We can also classify polynomials by their degree. The degree of any given term is how many instances of variables are multiplied within that term. For example, x^3 has a degree of 3, because it's x * x * x. The degree of the polynomial is equal to the degree of the highest-degree term. x^3 is the highest-degree term, so the polynomial has a degree of 3. In other words, it is a third-degree polynomial. One way to rewrite this polynomial is to order the terms from highest to lowest degree, which is often the standard way to write polynomials. x^2 + x^3 can be changed into x^3 + x^2. Another thing we can do is called factoring. Factoring is basically the inverse of distributing from the distributive property: instead of going from a(b + c) to ab + ac, you go from ab + ac to a(b + c). In our case, we can rewrite the polynomial as follows: x^3 + x^2 = x^2 * x + x^2 * 1 = x^2 * (x + 1) Like I said, this is basically just going backwards from the distributive property. if you want, you can verify for yourself that this works. One other common concept is finding the roots of a polynomial, or the values for your variables where the polynomial is equal to zero. Basically, "What number do I have to plug in for x so that this whole thing becomes 0?" You can solve this using an equation: x^3 + x^2 = 0 I'll rewrite the polynomial in its factored form from earlier, since that will be useful: x^2 * (x + 1) = 0 If our whole expression is equal to 0, that must mean that one of the two factors in it is equal to 0, right? If you multiply two numbers together and get 0, at least one of those numbers has to be 0. So we have two possibilities: x^2 = 0 or x + 1 = 0 For the first one, if x^2 = 0, then x must be 0. So x = 0 is one of the possible solutions, meaning it is a root of the polynomial. As for x + 1 = 0, we can solve this by subtracting 1 from both sides. We get x = -1, and this is the second root of our polynomial. Now to check our answers and see if they make sense. We can plug these values in for our polynomial. Let's start with x = 0: x^3 + x^2 = 0 0^3 + 0^2 = 0 0 + 0 = 0 0 = 0 Zero is indeed equal to zero, so that makes sense. Now for x = -1: x^3 + x^2 = 0 (-1)^3 + (-1)^2 = 0 -1 + 1 = 0 0 = 0 And this works once again. So our roots are x = 0 and x = -1.

[@edvinas5555]

@@isavenewspapers8890 HOLY SHIT- GET A LIFE. HOW DID U WRITE THIS *FOR A KZbin COMMENT*

[@Nkit_1]

last one will be x^8, not 16

[@latermyfriend8934]

No because there aren't parentheses on the x^4 which mean it's x^(4^2) (because the exponent has the priority), if there were parentheses such as (x^4)^2 then yes, it would be x^(4*2) which is x^8. Hope I helped.

[@Nkit_1]

@@latermyfriend8934 oh, so it was 4(square)? And not x(quad(sqare)).

[@jonathanSpg]

​@@Nkit_1 yes its squared

[@thepotassiumgamer2137]

No because 4² = 16

[@Nkit_1]

@@thepotassiumgamer2137 yah man i understood

[@XBGamerX20]

the last one can be tricky x^4^2 x^16 (x^4)^2 x^8 x^(4^2) x^16 (same as first)

[@idlesquadron7283]

yep

[@romaindautricourt4890]

but he wrote x^(4^2), there can be no doubt. On a keyboard it's a bit difficult to write it but it is clear that the exponent is to 4 and not to x to the 4. Otherwise there would be parenthesis like in the third example

[@_slimexd_1079]

well the way you write it can make it tricky in question you will be able to clearly see whether its square of whole or the power

[@pradeepguntha939]

❤❤❤❤

[@celebritiestv8151]

Badda bim badda boom boom boom❤

[@Kratos....]

I need confirmation thanks!

[@sssniperlion]

the dot means multiplication

[@isavenewspapers8890]

Indeed.

[@s_p_gaming_ex4201]

Are you sure about last one

[@isavenewspapers8890]

Yes. Exponents are evaluated from the top down.

[@souravmohanty1200]

thanks sir 🙏💯 ever

[@ShadowEditz68]

Someone tell me in the second one what that x1 is?

[@mohammadmorshedimtiaz3673]

Only x

[@isavenewspapers8890]

x to the 1st power, or "repeated multiplication" with 1 copy of x, which just gives you x.

[@MaranSamatham]

😮class topper

[@S64C]

x1 = x

[@souravmohanty1200]

thanks sir 🙏💯

[@nikitakhripun2029]

Did no one find the mistake in the last equation?

[@isavenewspapers8890]

There is no mistake. That's how exponents are supposed to be evaluated.

[@gianlucalepiscopia3123]

Last one is x^8

[@matteofontana_]

No

[@solitary6002]

No

[@random22453]

Never ever do math again

[@gianlucalepiscopia3123]

@@matteofontana_ you right, it's like x^(4*4), not (x^4)^2, as I wrongly thought. Bravo

[@matteofontana_]

@@gianlucalepiscopia3123 kekw

[@RSLT]

❤

[@arkdream1808]

これめっちゃ助かる

[@jncyfama]

The last one fooled me.

[@Autonomous123]

same I thought it was x^8 lol

[@forever_golfer1981]

I don’t get the radicals

[@XxjazzperxX]

You telling me that “power of” is right associative? What madman would do this?

[@SaqibRiaz-nr3zv]

How to we get 16

[@isavenewspapers8890]

4^2 = 4 * 4 = 16

[@m1nt137]

People saying this is 6th grade math, but really I'm in the middle of my senior years and we just started on this

[@TalkingBen757]

people who learned it in 5th grade

[@vusalsadiqov5602]

x^16

[@dannyfilmss]

i do this and im in yr 6

[@IAF60]

x ke power 16

[@kacperpawlowski1149]

That's the shorts I like to watch

[@animemchik]

Which grade it is in your country?

[@Movie_edits_]

Mine is 8th lol

[@animemchik]

@@Movie_edits_ omg it's 6th grade in my country

[@Movie_edits_]

@@animemchik it’s 8 for me 💀💀💀

[@lizzybach4254]

7th here!

[@Jrod7291]

Now add fractions, that’s gonna mess me up

[@suspicioustoast6919]

remember with division, x^3/x^3 is 1 not 0 lol

[@Vanduo610]

3-3=0 a^0=1

[@SHIN2024_official]

That's right. Any number divide by itself is always 1... except for 0.

[@sandhyaranidas1997]

Keep it up

[@ginnyhaokip2060]

what's the background music got to do with algebra

[@AmarjeetJoshi21]

Niche wala galat kiya x^8 hoga

[@lizzybach4254]

Are you in f*****g primary school?

[@깃털꽂은올빼미]

댓글들.. 거듭제곱을 몰라..? 좀 많이 충격인데..,,?

[@allmightyphonex3946]

In the second question youbdont need to rode 1 to x but is okay

[@reiniersmits703]

"X^1" why? just say X

[@isavenewspapers8890]

To demonstrate the rule.

[@cheefoong8923]

For all of you that are saying that the last one is wrong, you need to get a math tutor. The answer is correct as the question isn't (x^4)^2. To get the right answer you need to square the power of 4 to get x^16 Therefore, he is correct and you need to get a math tutor.

[@jaromirgaines7994]

No you multiply the powers not raise them. Therefore x^4^2 = 8, !=16

[@cheefoong8923]

@@jaromirgaines7994 use a scientific calculator my guy

[@mirkotorresani9615]

​@@jaromirgaines7994 a^b^c stands for a^(b^c). Exponantation must be red top to button

[@chrissystewart6268]

Woooooow I never learn this

[@AmanzholKuandykov]

😮😊😊😊

[@Pr0c3nt]

Dude uses a sound from 2020 💀

[@MaranSamatham]

I am a maths topper👩🏻‍🎓👩🏻‍🎓👩🏻‍🎓

[@DarkWinterAMV]

Am I the only one who doesn't get it but stayed for the song-

[@yslo]

this is middle school math

[@DarkWinterAMV]

@@yslo and you're assuming I may not be in middle school?

[@yslo]

@@DarkWinterAMV yeah pretty much

[@RoyTagliaferro-k2r]

It's actually pretty basic.

[@abdoboujarat9737]

If the 2 is equal to 4 in the size . Then we can told 4 multiplied by 2

[@ubaidahali5376]

how did you get the last one?

[@heisenburgeronthetoilet]

4^2

[@isavenewspapers8890]

Exponents are evaluated from the top down, so x^4^2 is really x^(4^2). Evaluating: x^(4^2) = x^(4 * 4) = x^16

[@milkywaygalaxy6088]

Really i learnt in grade 6 th

[@pjw-]

last one is x^8 because it’s literally just x^4 * x^4 which is x^8

[@si4h_3522]

x^(4^2)=x^16

[@pjw-]

@@si4h_3522 the default notation of x^4^2 is (x^4)^2 because of pemdas, so it is x^4 * x^4 = x^8

[@JakeAnthrax420]

Whats the name of the app

[@unfrendlyanimation]

I know

[@AzeTheOne]

theres no x¹ it will just be x

[@superawesomepayton6038]

There is an x^1 but it's just understood as x

[@jonathanSpg]

X^1 Is just x* So its correct And helps understanding the process

[@md.sourovhossain9048]

The last was wrong because "power and power are multiplied in index"

[@cjemanuel2645]

im in 9th grade my test starts a few minutes and omg it's gonna be so hard

[@kfjfkeofitorhf9520]

5X^2-6X-2=0 ชว่ยหนอ่ย

[@NpR222]

This algebra 1 test finna be easy ash ☻️

[@bikarsamiyasab8309]

16

[@parusramsamal6561]

8

[@jonathanSpg]

How Its squared not multiplication

[@Handsomeboi1]

Can someone please explain how the 4th problem is solved?

[@adityaashutosh3362]

In a variable if the power is rational, the denominator of the rational number gets to the root side, then the numerator gets to raised to power. For example- 8¼(8 raised to power 1/4) is equal to root4(8) raised to power 1.

[@adityaashutosh3362]

In the video, he just did the converse of this