(5 to the 6th ) - (5 to the 5th ) over 4 =? MANY will get WRONG! (No Calculator)

Powers and exponents problem with numbers and fraction - how to solve with no calculator.
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[@geoffdrew5207]

How to string out a 30 second problem for 15 minutes.

[@ciffman]

Yeah. Did it in my head in 30 sec

[@cav1928]

Yes in fact. I seee several videos of tenis guy AND always make the same.

[@sdweston8]

Hey, a man's got to make a living

[@danielboehmke4626]

Thank god for the fast forward button

[@sophiecollard9320]

Good for you to have this easy! It isn’t a given to all!

[@quadmachine8434]

Sir, I am 60 years old and love math but have forgotten the basic operations to solving problems, haven't really had to do these in over 40 years, I appreciate your videos, lessons to get me back to what I once could do! Thanks

[@MKA63]

Same here. Same vintage 😀

[@philwaters5654]

You are correct. I am blocking channel as solutions are too long and drawn out.

[@vineymushran8046]

5⁵

The same but a little bit more logical way: 5^6 = 5*(5^5) 5*(5^5) - 1*(5^5) / 4 = 4*(5^5) / 4 = 5^5 It's like 5 apples - 1 apple level math problem. :)

[@brianschuetz2614]

Exactly how I did it.

[@cliff481]

Yes, I see a picture and "notice" that (as you point out) 5^6 is 5 times bigger than 5^5 and transpose it to 5x - 1x over 4 = 1x or 5^5. I wondered if you "saw" that or "worked it out" if you see what I mean.

@@cliff481 I see this two ways simultaneously. As 5^6 and as 5*5*5*5*5*5. So, I can not unsee the fact that 5^5 or 5*5*5*5*5 is part of 5^6 like 5*(5*5*5*5*5). I hope it helped. :)

[@peetiegonzalez1845]

That's how I did it in my head in about 7 seconds.

[@olli1068]

If you use Apple(s), you are most likely not able to calculate this without a calculator. 😅

[@StevenVosloo]

Way to long winded .... just get on with it.

[@fatroberto3012]

Getting on with it doesn't make him any money. KZbin videos need to get past certain duration limits for monetization.

[@iamnotfooled]

I do wish you can be a little less long winded.

[@JBM425]

Agree. Even taking into account explaining the how & why, this could have been an 8 or 10-minute video instead of 15.

[@toriless]

He is trying to help others not good in math, I just skip forward a lot, ask KZbin. I am sure they notice it.

[@pedinurse1]

So my problem is that all of your tangents made me lose my train of thought. It was worse at the end, did not make sense.

[@Og-Judy]

Takes too long futzing with WRONG ways to solve. Needs to get to the point abd just show hiw to SOLVE IT.

[@toriless]

OCD

[@michaeld2662]

Dude, you RAMBLE ON! Get the hell to it already!

[@jeffwells641]

Is someone forcing you to watch this video?

[@michaeld2662]

@@jeffwells641 No. Sadly I stumbled on it and mistakenly thought it would be entertaining. It’s too hard to watch with all the bullshit drawings and windy commentary. I wont waste any further time with these vids.

[@toriless]

You know you have control of the video. Stop complaining and skip forward like I did. You are just ignorant and not a victim.

[@tomwalker9836]

15 MINUTES i'LL NEVER GET BACK.

[@thePronto]

Here, have mine. Just read the comments next time...

[@toriless]

I skipped forward, you know KZbin has a little control on the bottom. You seem to know nothing about how to use KZbin. Maybe that tutorial should be next on your list.

[@FoodNerds]

Did you get the answer correct right away? If not it’s your fault for watching that long.

[@Dee-sn5uh]

Thank you for explaining several ways to do each problem and taking your time instead of rushing through.This is excellent for young children just learning and also for senior citizens that are brushing up on things that they haven’t done in years!Teaching math so that the student really “gets it” takes a special skill!Thank you!

[@stompthedragon4010]

And for senior citizens not only brushing- up but homeschooling their grandchildren.

[@user-gx1rk8yw6l]

Another *excellent* point being made at 10:16 is "you have to consider who you're learning math from"! Kudos, @tabletclass 👍👍👍 I think that many/most of us are aware of the difference between being taught-by-rote versus being challenged to THINK. With the-LATTER as teacher, one can often IDENTIFY one's weak spots WHILE RESOLVING them. Well... if one takes the time to do so... 🙂

[@russellamaru5175]

Fun to work - bring back old memories of strugging in math classes many years ago. Thanks for the problems.

[@danielleclare2938]

This dude would take 100 years to teach you Grade 3 math...

[@colt4667]

Yeah - He's pretty long-winded.

[@jerry2357]

@@colt4667Pretty? Very!

[@Jcarolinajr]

Amen 🙏 much too much….DRAMA!

[@chgosatrap]

He's the reason we have self-checkout.

[@mompatimase167]

Good to digress and go on about a buntch of fluff.

[@bellanegrin3915]

You actually have to learn the rules. You cannot do math without really knowing the rules.

[@gbo7821]

This video (15+ minutes) is way way too long for the problem. The majority of the of the time has nothing to do with how to solve the problem. If you're watching these videos to help improve your SAT or ACT scores you'll never get there.

[@namperumalsamysubbanaidu6348]

Very boringexplanation

[@toriless]

except when n = 0, sure got tired of that caveat in algebra

[@21CA.Missions]

Thank You! I appreciate that your teaching method is geared towards students learning this for the first time.

[@TheREALDocRabbit]

Answer is E: 5^5, easiest to refactor the 5^6 into 5(5^5), then subtract the numerator which then yields 4(5^5)/4 which makes the answer 5^5.

[@spades1288]

Love your videos! You explain things so well. And your voice is very calming. 👍

[@noobynoob6856]

It’s funny how I know how to use all of these stuff but I just don’t know if I need to apply it in a certain situation

[@charlesflannery4610]

If you factor out 5^5 you get (5-1) in the parentheses which is 4. This cancels the denominator leaving 5^5.

[@proteus404]

It might not always be the right answer for solving math problems, but if I don't know right away what to do I will typically factor the numerator first then the denominator and see if it simplfiies the equation or allows for cross cancelling.

[@majorrgeek]

@proteus404 - and still struggling today?

[@MrMousley]

(5^6 - 5^5) / 4 It is very tempting to just say 5/4 but 'to the power of' doesn't work like that. So .. let's express 5^6 as 5^5 x 5 so that they are both 5^5 ((5^5 x 5) - 5^5) / 4 which is also (5^5 x 5) - (5^5 x 1)) / 4 which can be changed to 5^5 x (5 - 1) / 4 5^5 x 4 / 4 and 4 / 4 = 1 giving us 5^5 as the answer.

[@frenchimp]

"It is very tempting to just say..." is the kind of sentence which means you have no idea what mathematics is about.

[@MrMousley]

@@frenchimp It's interesting you should say that .. because my mathmatics teacher at school (back in the 70s) always used to say ''Now, it's very tempting to just say'' before going on to explain why something was wrong, and in this case I was just pointing out one of the things that people could get wrong before going on to answer the question. If you think that means that I ''have no idea what mathmatics is about'' then I won't do it again .. however, after 50 years, it may be too late to tell him.

[@terrimoore7431]

This was helpful. Thank you.

[@Og-Judy]

I put it in a calculator. Gives a actual 5^5 value 3,125 This is why this stuff is way super confusing to many. It doesn't answer as "5^5" . Many fail to see the need for such mental gymnastics

[@toriless]

E baby

[@seibertmccormick184]

I got it by making a chart of 5 to the 1st through 5 to the 6th. Then i just did the simple arithmetic. I couldn't remember how to work with exponents, but that worked and didn't take too long.

[@toriless]

It is quick, take half a minute out of a huge test. I know, I typed them out in a response.

[@ralphchristopherson782]

Appreciate your channel. Great to catch up on my math which I always made it harder to understand. ❤️

[@catherinewoodsellerbeckhor7560]

My goodness I must have been well taught all those years ago, it just comes flooding back….great mind stimulation.

[@chrish7336]

At first I didn't remember the process either until he started into it, then I was like... Well Duh!!.

[@catherinewoodsellerbeckhor7560]

@@chrish7336 I managed it in my head then checked if I was right.

[@Mark16v15]

As an engineer, I work with several people who didn't pay attention in math classes, but were somehow promoted to the next grade anyway. They think I'm some sort of math god because I can solve problems like this in less than a minute.

[@toriless]

Yeah, when I transferred schools for 9th grade they had me take the PSAT with the 11th and 12th graders. I did not know about the minus 40 or I would have had a 790 since I answered them all, as it was my lousy 760 beat everyone but 1 chicken senior who skipped a few questions. They let me take the advanced algebra after those results.

[@geriskater2657]

Easy! But great to learn how to explain math problem solving! Thanks!

[@nicholasriley3569]

Fast forward 12 minutes to avoid endless waffle.

[@jasonadamik2206]

He just goes on and on and on and on....... Zzzzzzzzzzz...lim 0 -> inf.

[@richardhole8429]

That is why fast forward is made available.

[@g95051]

John these are great. Nice refresh for me and many more I'm sure. Thanks so much for posting

[@giannaleoci2328]

(5^6-5^5)/4= 5^5(5-1)/4=5^5

[@severed5739]

Correct!

[@josebarata3164]

5 to the power of 5 is the correct answer.

[@topkatz58]

e) 5⁵ Factoring out 5⁵ yields 5⁵(5 - 1)/4 = 5⁵ × 4/4 = 5⁵ × 1 = 5⁵

[@toriless]

yep

[@mikeeiben3430]

Love these videos, but you really need to raise the volume somehow!

[@ajsaus4825]

5’’’’. You make it very interesting , thanks

[@earlhaywood4372]

The detail explanations are important to allow the mind to fully absorb the solution subconsciously.

[@ninthsunn]

i am now retired, it’s good to see these problems again. though i have to say, throughout the years, i never had to solve nor ever came across a problem that i had to use this operation. i still can’t think when i’d be using it.

[@user-gx1rk8yw6l]

GOOD & thank you!😁😁 At 1:22 a definition of "multiple choice" is stated: "1 of these is the correct answer". This means *exactly 1* correct answer, ie no less than 1 correct answer & no more than 1 correct answer. One can validly *DEDUCE* from it that "all answers except 1 are NOT correct".

[@toriless]

Then there is the D answer that is A & C are correct. Just not usually in math, 17 A) is odd B) is even C) is prime D) both A and C D is most right but the others are STILL correct so your hypothesis is absolutely wrong since only B can be eliminated. I assume you do not do well in tests.

[@user-gx1rk8yw6l]

@@toriless "you do not do well in tests" is not a correct assumption.

[@PlanetNumeracy]

Excellent explanation!

[@mohork]

Starts at 6min50

[@debunkosaurus8228]

I'm glad to know that my ability to do these in my head is not diminished.

[@donmoore7785]

Easy one. Factor our 5 to the 5th in the top, apply parenthesis, cancel the 4s.

[@thegreatbambino3358]

This took me all of 4 seconds to solve in my head. Thanks for the 15 min video

[@russelllomando8460]

great explaination. factor and solve. thanks for the fun.

[@user-ri6rn7ti5h]

Yes it was

[@mylittlepitbull3143]

Thank God this problem seemed easy to me. That means my brain still works.

[@ManekiNeko1972]

Here's what I did: 5^2 = 25, 25 × 25 = 625 (4th power), 625 x 25 = 15,625 (6th power). 15,625 - 3,125 (ans/5) = 12,500 Now that we know the top answer is 12,500, divide it by 4, you get 3,125 which, surprise, is the 5^5 answer we had earlier.

[@richardhole8429]

Fantastic. It is the harder way to do it but YOU got is right. Take that A+ proudly!

[@user-ek9ep6bs4s]

Vielen dank für deine hilfreichen Beiträge.

[@kelleeb7823]

why is your volume so low?

[@LjR40]

I thought it was me. I'm hard of hearing as it is. Tried to headphones.

[@aryusure1943]

@kelleeb Indeed! I left him a message as well.

[@truthcooperator4683]

What? It is really high.

[@jessiehogue.]

@@truthcooperator4683 It really isn't, lol. Maybe your headphones are highly sensitive, but at 100% with mine, I barely hear a whisper on this video.

[@toriless]

same for me

[@treespirit2000]

Meant to write: John, could you please turn up your volume. Thanks!

[@APP1E5]

When you have the division line , I was always taught the numerator and denominator were in separate parenthesis. IE 3+4 over 4*3 is (3+4)/(4*3)

[@toriless]

It is best practice, especially with computers.

[@nancyfloyd7052]

E. Factor out 5 to fifth power. Leaves (5-1 ), which is 4. 4 innumerator cancels out four in the denominator, leaving 5 to fifth power

[@user-cw9qn1nb2n]

I reckon the answer is f) = 3,125. Derived from: 15,625 minus 3,125 equals 12,500 divided by 4 equals 3,125. Simple!

[@phildavenport4150]

If it's not acceptable to the OP, somebody wants you to follow some rule that makes sense only to the person arriving at the alternative solution, and to the people who also follow that rule. There are plenty of similar maths puzzles online where people differ owing to their following different rules. Maths is NOT a black and white discipline, where there is only one correct solution for each problem. If you want to do well in maths class, learn what rules that particular teacher wants you to follow.

[@adamslaney5638]

lol 3125 is 5^5 so (e)

[@toriless]

Still the slow way, easy but slower.

[@rogergeyer9851]

@@phildavenport4150: Since 3125 IS 5**5, what the hell are you babbling about? It's NOT a different solution than all the comments using algebra, factoring out 5**5, and getting 5**5 as the answer. It's just doing the problem directly with good old basic pre-algebra arithmetic, like we did in middle school, 50 years ago.

[@stephaniedavis5773]

This is how I did it too. But the 3125 breaks down to 5^5 so that’s the answer I committed to. Which appears to be correct but this method seems to be incorrect?

[@raya.pawley3563]

Thank you

[@earlhaywood4372]

I find the lengthy explanations mentally stimulating .

[@pharmdiesel]

Good one!

[@areeratasudhasirikul952]

Wow! Very easy method!

[@Jabberwalkie-zi5tu]

I wish I had a Algebra teacher in JH like you, I failed. Come in college I had great teachers and did great but the things we worked on a Calculator wouldn't help you any(this was the 80's) unless you knew how to work the problem. Most of the "what is the correct answer" you see on KZbin are not formatted correctly so they create a argument, Mathgirl did a great video years ago covering this..

[@AsGangIII]

Please do this for me 🙏 Kate likes to walk down moving escalators and she takes one step at a time. When she walks down at a rate of 2 steps per second, she reaches the bottom from the top after 18 steps. When she is exhausted, she will walk down at a rate of 1 step per second and she will reach the bottom from the top after 12 steps. Find the time- taken for her to reach the bottom from the top if she just stands on the escalator.

[@toriless]

Depends which way the escalator was moving but maybe forever.

[@davidhayes2928]

Audio was to low to hear anything.

[@igelkott255]

yeah, I kept thinking of the scene in Blazing Saddles when the teacher was speaking too softly and everyone complained and then she started yelling.

[@jessiehogue.]

Same.

[@waynekasmar4401]

Spelling was too wrong to understand.

[@myvmix]

Tip..... If you want to help anyone in maths.....1. Get to the Point , 2. Get to the Point , 3. Get to the Point!!! Stretching a 1 minute session for 15 mins or more would take people many years to get past junior grade at that rate !!!!! Most people including myself would much prefer a direct simple approach rather than take a walk around the garden to see what's there!!! You're not helping anyone stringing them along like you are!!!

[@graemerose1616]

or he could just to the point, dragging things out does not help people poor at maths.

[@Mal1234567]

I solved it in my head this way: factor out 5^5 from the numerator to get 5^5(5^1-1). That leaves 5^5(4)/4. The fours cancel out to 1, leaving e. 5^5.

[@marypostlethwaite5234]

Ok so I am 50 yrs old and math has never been my subject. But let me say in this one video I learned more than I have known all these years. Somehow you made it so easy for me to understand. Thanks.

[@ladyjade001]

I never understood powers math and after watching this 5 times I’m still confused. Would you make one that only goes through the solution the correct way? I’m 70 & have never had to deal with powers except in math classes. That said, I’d really like to know how to do it. I vaguely recall a math teacher saying something like add the exponents together. I just don’t remember why.

[@michaelzoran]

3,125 was the answer I came up with while doing this calculation in my head. I was correct. Although, this answer of 3,125 is not an option in the video. The video shows the answer is 5^5. This is correct. However, 5^5=3,125. So, the ultimate answer should be 3,125.

[@toriless]

They wanted you to apply the logic he demonstrated rather than plugging away at the math, I agree it does not take much longer but the question is testing n=your ability to for application not how fast you can multiple. I was working it out and pause when I saw (5-1) / 4 which equals 1. I did the multiplication in my head and then saw this relationship which you missed.

[@richardhole8429]

Both are correct but only 5^5 was given as a possible answer.

[@davidbrown8763]

So easy, did it by inspection in my head.

[@matikramer9648]

Thank you Remind myself sometimes of math is useful

[@christylumpa4357]

Awesome!

[@tomtillett9309]

It seems to me that you have not used PEMDAS once you get to 5 to the 5th ( 5-1) as you should solve P, Parentheses prior to the 5 to the 5th. Leaving you with 5 to the 5th times 4.?? Also, how did you derive the five and the 1, in the (5-1)???

[@user-zu7zr9ui3u]

why did you add the powers of 5 to the 5th and 5 but did not add 5 to the 5th and 1? does that mean 1 does not have an assumed power?

[@mattparoz4246]

I used a calculator cause my brain doesn’t brain real well sometimes and I got 3125, which turned out to be A correct answer, but not the answer your looking for. It’s the same as Hello is to G’Day is to Hi, different words, same intent.

[@toriless]

5 25 125 625 3125, 15625, it is easy to do without a machine.

[@seibertmccormick184]

I got it, and it took just a couple of minutes. But I'll have to watch and figure out why.

[@davaogary7042]

I got stuck since I was thinking of PEMDAS. I was attempting to do the division somehow before the subtraction. Guess that is why I gave up after basic emementary algebra.

[@Og-Judy]

Why? Exponents come before division in PEMDAS . Think of 5⁶ -5⁵ as (5⁶-5⁵)/4. You have to simply the 5⁶ - 5⁵ first before any division

[@toriless]

What does the E stand for in it, EXPONENTIAL

[@snjobvu22]

enjoying your lecture

[@m-k-g-w]

I think the easy way was much harder, for me anyway. I watched it three times, but of course this is a refresher and boy have I forgotten a LOT! Thank you though, I watched this 3 times and I will persue your videos. Math was my All time favorite subject all through school. 😀

[@fitchcarl]

Such muttering, cannot hear, even with volume on high...

[@user-ov4zk6gb3i]

He speaks in prosody. Monotone is a vocal utterance that is a single tone without variation in pitch or harmony

[@timothybloomer4246]

Take out a multiplier of 5^5 from the top and it falls into place easily.

[@majorrgeek]

not correct way

[@matswessling6600]

@@majorrgeekoh yes it is. that IS the way.

[@majorrgeek]

@@matswessling6600 - you cannot subtract a multiple - the correct way is to follow BODMAS and you never go wrong

[@matswessling6600]

@@majorrgeek noone said subtract. "take out" here means "factor out". as in 5^5(5-1)/4.

[@majorrgeek]

@@matswessling6600 - then next time say "factor out" instead of take out

[@timothylunde]

Start at 13:30

[@paulembleton1733]

In secondary school (UK 1970s) I failed maths because I couldn’t show my workings in a mathematical way. Here I guessed E simply because the other options look to small. Even 5^4 because the difference between two powers is larger than any smaller power, and we’re dividing by a number that’s less than the base. If I were asked without options then no chance, but I’m a programmer and there are maths libraries🤫

[@colinmccarthy7921]

It’s not what you do,it’s how you do it. There are Rules to follow.

[@clickpositive]

Why do all the 'sums' simplfy then compute 5^5

[@HotRot89]

Pull out 5^5 out of the bracket. It becomes 5^5*(5-1)/4 so it resolves to 5^5

[@endthefed5304]

Yes. Took me about 10 seconds

[@toriless]

That is what he did, watch again

[@HotRot89]

@@toriless I didn't even watch it a first time lol

[@mikejackson2472]

Shouldn’t it have been divided by 4 before doing the subtraction

[@_MrL_]

Did this in my head in less than 30 seconds using the long way, got 3125 so picked E … Would have used your method if it wasn’t a simple number like 5’s … 5’s are too easy to do in your head! … In my head I multiplied by 10 then divided by 2 …. 5*5 =25 250/2 = 125, 1250/2=625, 6250/2=3125, 31250/2=15625 …. Took the 3125away from the 15625 easily in my head to get 12500 then just halved it twice 6250 then 3125 which was the 5th of my 5’s so got 5to 5th in under a minute with no writing down … does this make me weird? Doubling and halving is too easy … even the subtraction was easy … so I chose the easiest option.

[@KipIngram]

Well, 5^5 is (5^3)^2 = 125^2 which is going to be up around 15,000. 5^5 will be a fifth of that, or around 3000, subtracting it brings us down to 12000-ish. Divide by 4 gets us to 3000-ish. 5^4 is 25^2 = 625, so the only answer here remotly big enough is e, 5^5. It took me a lot longer to type than than to think it - I probably went through it all in 6-7 seconds.

[@pretzelcoatl_1121]

Factor out 5^5 and you’re left with 5^5(5-1)/4. 5-1 is 4 divided by 4 is 1 leaving 5^5

[@ianbrooks4516]

So, I wanted to try this as I couldnt remember how to do it. So what I did was 5^3 - 5^2 to keep it simple and because I know the numbers at 125 - 25. So the answer is 100, which is the same as 4 x 5^2. Which means that 5^6 - 5^5 = 4 x 5^5 I realise that 5^6 is just 5 x 5^5, but my brain didn’t jump to that. It clearly wanted an easier version to work with instead. So 4(5^5) / 4 is just 5^5. So the answer is ‘e’.

[@toriless]

You actually complicated it.

[@systemchris]

11:55 for the actual method

[@cosimo7770]

Mental arithmetic in 3 seconds. Numerator = 5^5 (4). Hence e).

[@Tahgtahv]

I was kind of embarrassed at almost getting this, but thinking the answer wasn't listed. I had factored out the 5^5 and then forgot about it and thought the answer was 1.

[@stonerdave]

Clever equation- I’m going to try to answer without watching- 5^6=5^5•5 so subtracting 5^5 from 5^6 will equal 5^5•4 and dividing that by 4 will leave 5^5

[@annamelendrez8929]

Love the calculation

[@victorfinberg8595]

should be "trivial" for anyone who has taken ANY math at the post-secondary level. why? because you need to understand algebra, and you need to be comfortable working with numbers.

[@llywyllngryffyn8053]

The answer is E. 5^6 = 5 * 5^5 = 5^5 + 5^5 + 5^5 + 5^5 + 5^5. If you subtract 5^5 from that, you stil have 4 of them. divide that by 4 and you get 5^5.

[@spryteXO]

Even doing this the long way, ie multiplying it out, powers of 5 are very easy without using a calculator. Maybe an extra 10-15 seconds compared to the easy way.

[@toriless]

Yep

[@gopherspace8571]

Learn so much from your videos Thanks for doing this . What would you say is the ratio of grateful people to ungrateful ? Just a rough estimate I really want to know. ❤

[@scottabroughton]

This video is more about test-taking psychology than solving a problem that takes seconds (if you have actually learned how to solve these types of problems).

[@someguyfromafrica5158]

(5 to the 6th) - (5 to the 5th) = 5 * (5 to the 5th) - (5 to the 5th) = 4 * (5 to the 5th). Dividing that by 4 gives 5 to the 5th or (e).

[@waynekasmar4401]

It's easy when you think about it in concrete terms. 5^6 is 5 times more then 5^5. Take away one of those 5 times and you are left with 4 of them, which leaves you with just one when you divide them by 4. And we know that has the same value as the one we took away, which was 5^5.

[@toriless]

Same idea, just backwards

[@robertroemer4233]

Mic volume level drive is too low

[@relaxingwindow6137]

I'm super lazy, so I solved 5 squared minus 5 to the first divided by 4, which is 5 to the first.

[@dough9512]

When you factor 5^5 out of 5^5, you really don't get one, you get 5^0, which is equal to one. ANY number to the zero power is one. Even zero, if I remember correctly.

[@stephenandrew6410]

e: 5^5