4 to the (3/2) power = ? many don’t know what to do! (NO Calculator)

How to find the powers of numbers with exponents as fractions - rational exponents.
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[@George-ci5jz]

90 and enjoy keeping the mind sharp.

[@rianmacdonald9454]

I am new to your channel, and seeing it makes me very happy. I am a life long huge lover of MATH, and seeing you spread math like this makes me very happy. I have scrolled through so many of the comments on your videos and the amount of support and people getting to know math from you r work is very up-lifting. Please keep up this great service of knowledge sharing that you are doing. Wish you all the best buddy.

[@Tigerpili]

I appreciate that you showed how to do it on a calculator, and the defining of terminology! Thank you!

[@andyt.2240]

I love love love how you make the seemingly difficult simple 🎉…That’s why my 3 kids love your teachings as well…👍🏻

[@gregwessels7205]

Haven't seen this in 45 years, excited to re-learn it.👍

[@seibertmccormick184]

I had forgotten some of this. I never really learned some of it. Thanks.

[@mauriziograndi1750]

1) Use the denominator of the indice to find the root of the base (SQRT of 4 = 2) 2) raise this result to the power of the numerator (2^3 = 8) Answer = 8

[@af4od02]

I recently found your channel. I was never a math whiz. But, I am enjoying learning from your teachings. I am going to have to rewatch this video a couple more times to really comprehend it. Thanks.

[@carollomax9524]

Me too!

[@Geoff_G]

You really should explain that there's two ways to look at this. 4³/² = (4³)¹/² OR (4¹/²)³ are both correct and equal to each other.

[@BobbyJardine-vs8yc]

Thank you, this is the missing link for me.

[@davidg4288]

I actually cubed 4 (and got 64) then took the square root of that (and got 8). I was all proud of myself for getting it right without realizing there's an easier way still using smaller numbers.

[@harrymatabal8448]

My Geoff, use what ever method you want but the answer is 8

[@harrymatabal8448]

Mr David your method is perfectly correct

[@mj3845]

This kind of problem is something I'd need to review. I'm sure you explained it well, I need to study the steps a few times.

[@ericbaca9744]

I'm new to your channel and have never had such well thought out explanations of algebra taught. The way you utilize the board is in it's self half of the greatness you provide. Thank you for sharing the knowledge with us. I usually follow along with a sense of understanding, but I have to tell ya, this problem went right over my head... Hahahaha 😂😂😢 I usually watch the same problem more than twice just to fallow the solution, but this one will be minimum five timer. ; )

[@davidmacleod9313]

3:00 Is there such a thing as “recreational math”? Lol Love this!

[@bobwineland9936]

X^a/b =bth root of X^a. So the sqrt of 4^3 = sqrt of 64 =8. Another approach would be to let 4^3/2 = 4^2/2 * 4^1/2 or 4 times the sqrt of 4=8.

[@russelllomando8460]

Cool thanks. In high school, in 1965, I never had rat exps. Fun...

[@nigelmansfield3011]

Of course, 4 cubed is 64 and the square root of 64 is 8. I prefer that method for more complex roots but either way works.

[@deograciousuwiragiye8429]

Law of indices Squared root of 4 power 3 2 power 3 2×2×2 8

[@ianclampin103]

I love the channel, however I have never seen this in all my 65 years, even at school so I doubt I need to learn it now,😀

[@danieldennis9831]

√4^3=8 And that works weather you first cube then do root or do the root and then cube.

[@Dani-ICU-RN]

4:15 oh play ngom, how do you know to jump straight to √ 4

[@wagnermh1202]

Can we do like this 4 x 4 x 4 = 64 / 2 square = 8? Is it always X multiplied by the Y potence and divided by the root of radical Z?

[@LA610]

PS I tried to use log on it as well

[@frankinga3120]

Agreed; the question is ambiguous. IMO the literal meaning is that only the "number" is multiplied by 3.

[@athletixbc]

Figured it out in my head using a slightly different technique. 4^3/2 =(4^1/2)(4^2/2) =4^1/2 * 4^1 =2 * 4 = 8

[@thomassicard3733]

Oh, yeah... forgot about that stuff... makes total sense.

[@unclejoker9975]

I haven't seen this in over a decade. It took a moment to realize how this works.

[@davidmacleod9313]

2:26 Hey! My calculator is fresh out of carrots! Dollar store…ugh. I do see the square root sign, though. 😊

[@Dani-ICU-RN]

2:15 I'm pretty smart.. and good in math, but I'm confused on how you automatically know to have to square the bottom number what if it was 5

[@nigelmansfield3011]

5 on the bottom would mean 5th root.

[@sylviawagner2859]

would taking 4 to the first power times the square root of 4 work for this problem. That's how I solved it and got the same answer.

[@elsfane]

The steps looked complicated so I used 4^(3/2) in a calculator or google instead.

[@vamsm]

4 to the tried power and then the square root of that produces the result.

[@gryffn8860]

Love watching you make math fun. I have one question though… how do you tell the difference between 4 3/2 power vs the fraction of 4 3/2? Isn’t that an issue for people? Or am I just dense? 🙂

[@cheriem432]

gryffn8860, you are dense. No, you're not! You can tell by the way it is written. exponents (powers) are written slightly above and after the number. The mixed number is all written on the same line.

[@JohnDoe-ok5wo]

Also: (4^3)^1/2

[@devonwilson5776]

Greetings. Yes, I can figure it out without a calculator. The answer is 8. We determine the value as follows , it is the square root of 4 raised to the 3rd power = 8.

[@harrymatabal8448]

Excellent Mr devon

[@devonwilson5776]

@@harrymatabal8448 Greetings. Thank you kindly for your holiday wishes. Happy holiday wishes to you and your family also. Have a safe, wonderful and joyous holiday. Going forward, I also wish that the new year will bring you and your family continued success and prosperity. God's richest blessings in all your life's endeavours.

[@shahrouzzarringhalam2385]

That was hard for me.

[@Kirke182]

I did it by turning 4 into 2^2. So, 2^[2 (3/2)] which is 2^ (6/2) which is 2^3 = 8.

[@davidmacleod9313]

That you, Professor! 😊

[@doubledee9675]

It's not so much not knowing what to do, but rather wondering why anyone would want to do it......

[@tracyzitzelberger5263]

Why isn't it (-8) as well? Thanks.

[@createinmeacleanheartohgod6871]

I don't need this calculation when i do stock market trading 😂.

[@susiekinpgh4008]

I GOT IT!!!

[@WombatMan64]

I used a different property of powers to get the same answer. xᵃ⁺ᵇ = xᵃxᵇ... Easy enough to visualise, x²x³ = (x.x) (x.x.x) = x.x.x.x.x = x⁵ 3/2 = 1 + 1/2, So 4³/² = 4¹ x 4¹/² (Sorry, my superscript converter isn't converting the "/", just imagine that up there as well) = 4 x 2 = 8

[@brianburnside5949]

Exact same way I did it.

[@alcorgarcia619]

(sqrt4)³=2³=8

[@ajsaus4825]

8 John

[@peace-now]

Could be -8 too.

[@seibertmccormick184]

Thanks. I didn't get that one (I got 16) but I'm learning. thanks.

[@fredludwig2241]

I would suggest that MOST people don’t know what to do.

[@aryusure1943]

3/2, if we simplify, equals 1.5. So I used the PEMDAS rule to simplify 3/2 which gave me 4 powers 1.5 = 6. Obviously I was wrong. So if I understand well, when you have a fraction as the exponent you have to apply the radical to the base first in order to procede further with the solution of the equation and it's a universal rule. Did I get this right?

[@discobear5752]

You can do the numerator and denominator in exponents in either order. If you first do the cubing, then take the square root, it goes like this: 4 x 4 x 4 = 64 and the square root of 64 is 8. If you first take the square root, then the square root of 4 is 2 and 2 x 2 x 2 is 8. Same answer either way.

[@gbhxu]

@aryusure1943 6 here too doing your method I even get the answer as 4 (4x4x4)/(4x4) Probably another one of those ambiguous equations. Depends where and when you did your maths as to what answer you get

[@discobear5752]

@@gbhxu 4 to the 1.5 power is correct. 4 to the 1 power is 4. 4 to the .5 power is 2. Multiply those two parts together, 4 and the 2, and you get 8.

[@darkwitnesslxx]

​@@discobear5752Aha! This is where I went wrong. I too instinctively thought of 3/2 as 1.5 and knew that 4^1 is 4 and that 4^.5 was 2. But then I added them together to get 6, when I should have multiplied them to get 8. Thinking about it logically, I understand why multiplication was correct, and not addition. Thanks.

[@aryusure1943]

@@gbhxu Now that I think of it I know why our method can't work. Each time there is an exponent the base is multiplied by itself first and any number of times as the exponent. The base is not multiplied by the value of the exponent. As for where I did my maths, please consider first the "when". ;) I have not did maths since over 40 years. But I like testing my memory. The difficulty here, obviously, is those stressful fractions. 😮

[@Music--ng8cd]

Would it be +/- 8?

[@mathewhorodner2000]

principal square root - looking for the positive value......"The principal square root can be found by first finding the square root of the number, and then only selecting the positive answer."

[@thomassicard3733]

4^3 = 64. Sq. root of 64 = 8.

[@lukewalker1051]

for those learning math....answer is simply the square root of 4 cubed. For those learning this stuff, don't be plussed. Its all practice like learning anything from the guitar to changing hands on a wrist watch.

[@martinhutton6294]

Surely 8 is only one of the two answers - (Root 4 = + or - 2. +2^3 =8 and -2^3 =-8

[@vee8217]

2^2(3/2) =2^2×3/2 =2^3 =8

[@davidmacleod9313]

2:09 For me…maybe I needed to see that the sq root of 4 is 2 stage. Or did I miss my stage? Lol Okay okay…I’ll catch up.😊

[@docalexander2853]

How about 64 divided by 8= 8

[@docalexander2853]

4 x 4 x 4 divided by 4 x 4 = 8

[@topkatz58]

4^(3/2) = √4³ = √64 = 8

[@giannaleoci2328]

Rq(4^3)=Rq( 2^6)=2^3=8

[@Dani-ICU-RN]

Omg..I THINK so.. but before I look at the answer I'm going to get my sixteen-year-old to check my work LOL

[@josiegraham2591]

5 1/2

[@velikijoxotnik]

sqrt(4^3)=sqrt(64)=8

[@BobbyJardine-vs8yc]

It's either 32 or 8 or 6.

[@BobbyJardine-vs8yc]

It makes most sense to say 6.

[@victorcaldwell2900]

8

[@TheSimCaptain]

Why do so many who comment on these videos just repeat what the videos show without adding anything extra?

[@kalyankumarsarkar]

4^3/2= 4^3÷4^2=4^3-2ie 4

[@judyr9567]

On a roll.... haven't gotten an answer right. Ok, 5 1/2 ?

[@louise7552]

❤ well done, we are both brilliant. 😅

[@JamesReyes-bn4qg]

8 or -8

[@richardcommins4926]

I said that 3/2 is 1.5 or 1+1/2. Then I said X^(a+b) = X^a * X^b. Then I substituted in 4 for X and got 4^1 * 4^1/2 and got 4 * sqrt(4) = 8 . My point is X^(a+b) = X^a * X^b comes from the basic definition of exponents and X^(a*b) = (X^a)^b is a proof of (Log X^(a*b) = a*b log X and Log (X^a)^b = b log X^a = a*b log X) and is not obvious. You skipped over the proof and just made it so. My way is much easier to understand from basic exponents that we were all taught. (10^2 * 10^3 = 10^(2+3) = 10^5)

[@charlottecampbell8183]

8 ?

[@paulhaye]

4/1 * 3/2 = 12/2 = 6.

[@kevincoady8670]

Eight

[@sergiussouth4754]

24?

[@andrewgarcia-pt9fi]

5 1/2✌️

[@paulgerry2464]

4

[@hawkeyeinthehouse2995]

The answer is 4. 😊 .

[@asmahkidwai]

8

[@MrMousley]

Before I watch your video .. I could be completely wrong here but isn't 4 to the power 1/2 the same as saying the square root of 4. So .. 4 to the power 3/2 is the same as .. (the square root of 4) cubed which is 2 cubed .... which is 8

[@b213videoz]

4³/² = 64¹/² = 8

[@kennethwright870]

4^3 is 64, square root of that is 8

[@argonwheatbelly637]

8 in about three seconds. Sorry it took that long. 😔

[@MrDutcher]

This was painful to watch. I had to keep on jumping forward until you actually explained the answer at the very end, which is all I wanted to know. I still clicked like because it is educational for folks who don't already know how to use roots and exponents.

[@bobcornwell403]

I came up with 8.

[@gerontodon]

I got 8 by thinking of it as the square root of 4 to the power of 3.

[@harrymatabal8448]

Excellent way Mr geront

[@billthorburn7476]

6

[@fransalivar9815]

36

[@davidmacleod9313]

2:26 Jeez! I swear I’m not one of these students that always has something to say…but, in my defence…I’m having a double latte and feel rather chatty. Sorry!

[@powellmountainmike8853]

I have begun to remember why I detested 2nd year algebra/trigonometry in high school. They taught to the stupidest in the class and bored the living 5H17 out of me. I barely squeaked by with a C because I did so badly at trig. In the Navy they taught it quick and dirty, and gave us a horse to remember the sine, cosine, and tangent formulae, Sally Can Tell Oscar Has A Hard One Al;ways. I had no trouble with the trig I needed to solve for inductive and capacitive reactance or resonance. You OVER explain things, and bore the crap out of me.

[@LoneRiderz]

Or ²√4³ = ²√ 4×4×4 = ²√64 = 8

[@jeffyarlett5791]

Seriously 5 1/2

[@jeffmiklitschmiklitsch1177]

Answer 10 the salt will flow reeeeeeeeeeee reeeeeeeeeeee

[@jessejames8926]

Whaaaaaaaaaaaaaaaaaaaat !!!!!!!??????????

[@aaaaaeiou]

I cannot follow your explanation because it is full of WHY

[@evierice2230]

Nutso!

[@bjre.wa.8681]

I got the volume on max and can't hear you so your instructions come across as jiberish. You talk to soft or not recording as loud as necessary.

[@Rood67]

He talks so slow, playback at 2x and learn how to work this out in half the time.

[@LA610]

your examples were great in the second part but you glossed over the first part and lost me. fyi

[@rustyknott-W.D]

Three Halves? No such thing as three halves of a whole(those would be thirds, dummy). Heaven help us if you are a math teacher that doesn't understand that simple concept. Gimme a break. Ok, 4^2=16. 3/2=1.5, that's the exponent. So, now we know that 16 x 0.5 = 8. The utile way of writing this equation would be (4x4)/2, or (4x4)0.5. Why do you needlessly complicate the obvious?

[@josgalgebra3784]

(2^2)^(3/2) 2^(2(3/2)) 2^(3) 8 Students who study basic algebra soon understand what to do.

[@MeowMeow-cu2dx]

You are way too long-winded and should be more concise.

[@akhilkarthik1346]

You take too loong to introduce you and your concepts which made mee so arrogant 😤😤

[@trevorconnors1544]

Can you tell me why you pronounce pemdAs as pemdOs (is it an American thing ??). It is very annoying !!

[@saiedahmed5289]

8

[@michaelmorkert4623]

6

[@terrynoon8467]

8