8 to the 2/3 power times 9 to the 1/2 power =? Do you KNOW Rational Exponents?

How to simplify an expression with rational exponents. Learn more math at TCMathAcademy.....
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[@thomasharding1838]

Okay so without watching, 8 squared is 64, cube root of 64 is 4. 9 to the first is 9 and the square root of 9 is 3 so the answer should be 4 x 3 = 12. A lot of students that have issues with math watch your videos and I am sure that the detailed instructions and procedures you provide will help them get through their math difficulties. Keep up the GOOD WORK!

[@vincentrobinette1507]

I solved it in exactly the same way!

[@johnnyragadoo2414]

I wanted some review so I did it the hard way. I calculated the base 8 log of three, added 2/3 to that, and raised 8 to that power. Interesting observation - the area of one side of a cube is the 2/3 power of its volume. If you want the 2-d projection of a 3-d object, you raise the volume of the object to the 2/3 power.

[@scimitar415]

for some reason this self styled "utube mrmathman" lesson has all the qualities of an infomercial

[@shoman7205]

I rewrote 8 as 2^3. As 8 was originally 8^2/3 I now have (2^3)^2/3, I multiplied the exponents which will cancel out both 3’s, leaving 2^2 = 4. 9^1/3 = just 3. 4x3=12

[@zembalu]

Exactly! It took me a few seconds. But this only works for examples with integer roots without a calculator. Hence, the title correctly says "... an expression with..." and not "... any expression with...", which mislead me kind of. Should have read this twice :-).

[@RamasamyArumugam1927]

Thank you, Sir. I have subscribed to your wonderful channel of mathematics

[@MrSeezero]

First you attempt to get both sides to have the same exponent. If you are able to do that, then you can simply multiply the two bases together and enact the matching exponent as best as possible afterward. If you can't get matching exponents, then you just do the two sides separately and multiply them together afterward. It appears here that you need to do the latter.

[@يوسفحسينعبدالله-ز4ج]

d) 12

[@michaeltimpanaro5622]

Please, less talking. You used about 1/3 of a class for this problem.

[@MargaretCutt-um8iq]

YES! the extraneous stuff really just confuses me.

[@richardhole8429]

It took me just a bit of time going down the bunny trail of CubeRoot of 8^2 × 3 Then the DUH! Moment CubeRoot of 8, squared × 3 It should have been a 10 second mental exercise.

[@krunoslavregvar477]

😂☕🤣☕😂

[@alext8828]

Excellent....again.

[@warblerab2955]

I hope he does a video sometime on negative numbers with fraction exponents. I am a bit confused by them.

[@KW-gb9cd]

They're basically the opposite of whole-number exponents. Example: x^2 = x squared, while x^1/2 = square root of x.

[@dazartingstall6680]

Your comment got me thinking. And my first thought was "ouch," but I couldn't get rid of it, so I made a few notes to try to organise things. (And I'm assuming we want to avoid imaginary numbers. Because I prefer to keep my head unexploded.) While stressing that I'm in no way a mathematician, so I might be talking pure codswallop, here's how it looks to me.. When dealing with negative numbers: We can take the nth root if n is odd. We cannot take the nth root if n is even. Even-number exponents produce positive results. Odd-number exponents produce negative results. So basically the goal is to avoid having to take an even numbered root of a negative number. exponent is even/even: Raise to the numerator first. That gets us a positive result that we can then take the root of. exponent is even/odd: We're fine. exponent is odd/odd: We're fine. exponent is odd/even: We're screwed.

[@dazartingstall6680]

@@KW-gb9cd Except there is no real-number square root of x if x is negative.

[@chamberizer]

8 2/3 I took 8 squared = 64 I took the cube root of 64 = 4 Same answer just achieved it a little different. 4 x 3 = 12

[@danielwarren7110]

haha never seen it done that way before... interesting going to be playing with that all night.

[@chamberizer]

@@danielwarren7110 Ok - Thanks

[@danielwarren7110]

@@chamberizer makes sense though it is just the reverse of the way i knew how to do it. you do to the Numerator power first and then root by the Denominator power i do root to the Denominator first and then power by the numerator... now i sat and thought about it makes sense why it works still fun though so thanks.

[@chamberizer]

@@danielwarren7110 Either way it seems to work

[@aryusure1943]

Can you make a video with numbers we can't square without a calculator. Ex: 7 to 1/4 power TIMES 5 to the 1/2 power. Thanks in advance.

[@gopherspace8571]

Amazing. Thank you so much for what you do and taking the time to make sure that you hope we can understand it. When people say you're to windy, forget that man. People like me that like to learn need the extra help in understanding it. Yeah you forget about those smarty pants haters. From now on ok? Great lesson I learned a lot . I'm gonna give you a 👍💪👋😁😎❤️🌎 Thanks again

[@mysticmouse7261]

The 'rational' exponent can also be read as xm/n = n√xm

[@ecromancer]

Sqrt(x²) = abs(x). It is not x.

[@danielwarren7110]

^?/3 cuberoot then power of ? so cube root 8 squared & ^1/2 is same as square root so cube root 8 is 2 (*2) times squareroot of 9 which is 3 so 3*4 = 12

[@Kleermaker1000]

This is cube root of 64 x sqr. root of 9 = 4 x 3 = 12.

[@raya.pawley3563]

Thank you

[@johnmarchington3146]

8 to the power of two thirds is 4 and 9 to the power of a half is 3, so the answer is 4 x 3, or 12, i.e. (d).

[@MargaretCutt-um8iq]

Would 8^2/3 also be "cube root of 8^2" (I don't know how to write that on my keyboard, hope someone understands)? I get the same answer...or was that just luck?

[@vespa2860]

That's how I did it. John's route is fine too. cube root 8^2 So you could square the 8 first and then find the cube root of the result But 8^2 = 64 and the cube root is not immediately obvious (to me, at least!). While cube root of 8 is much easier which is then squared. I'm lazy and will tend to look for the easiest route. I think John was keen to show the relationships of fractional powers to equivalent roots.

[@gillianrolland4305]

​@@vespa2860taking the easy route is smart not lazy

[@MrMousley]

Easy bit first ..... 9 to the power 1/2 is the square root of 9 ..... which is 3 8 to the power 2/3 ...... cube root of 8 first ...... which is 2 ... then 2^2 = 4 which leaves us with 4 x 3 = 12

[@Shay-q8u]

First Part 8² is 64 so 64 to the 1/3 power: (4 * 4 * 4) ^ 1/3 = 4 Second Part 9 to the 1/2 power (3 * 3) ^ 1/2 = 3 New Problem 4 * 3 Final answer 12

[@bigdog3628]

super simple when you have a fraction as an exponent we use the numerator as a power than the denominator is the root we want. So in this case the First term is ∛8² which is ∛64 which is just 4. second term √9¹ which is √9 which finally reduces down to 3. 4 x 3 is 12.

[@deograciousuwiragiye8429]

8 to 2/3 power =2 power 2 2 is from racine cubic of 8 2 power 2 is 4 9 to 1/2 power = racine spuared of 9= 3 4×3 12

[@andrewsniimensaamoo253]

The answer is 12.

[@Eleuthero5]

Cube root of 8 is 2 and that squared is 4. Square root of 9 is 3. Quod erat demonstrandum.

[@mlgoldberg]

You spent 21 minutes solving a 2 minute question! Why?

[@MrSummitville]

Because ... That is what he does.

[@russelllomando8460]

got it 12 cube rt of 8 sqrd X sq rt of 9 thanks for the fun.

[@stompthedragon4010]

I HAVE NO IDEA! So I'll just watch

[@Serendipity7032]

You obviously know a lot about math, I wish you would talk less and just show how to get to the correct answer! That is how , I’m sure, you will help more people!

[@SandraDevant]

Agree

[@harrymatabal8448]

Mr serendipity. I just love your comment about this asshole😂

[@1234larry1]

He try’s to help students solve problems of the same type.

[@MrSummitville]

​@@harrymatabal8448There is something wrong with *YOU* . If you don't like the channel, then why are watching?

[@chrismcgowan3938]

yes its (d) This took about 10 seconds

[@seibertmccormick184]

I got 12, but I have to admit I wasn't sure. But I see everybody else got the same answer.

[@areeratasudhasirikul952]

d. 12

[@deograciousuwiragiye8429]

Square root of 2^2×3 =12

[@georgew.5639]

I guessed correctly.

[@lets_go_see_]

i ave subscribed for some time but visit your site only once in awhile. Please take this comment as a constructive dialogue i think you have quite a lot to share. Where i lose it is in the seemingly way in which you speak to the audience. We are young and in my case older folks. You speak to us like we are 5 year old children. Play back this episode for yourself and close your eyes while listening. Other than that, i would not have minded you as a math teacher, provided you got rid of that, "okay children" voice... Ttfn

[@richardhole8429]

You may try other sites which do not try to teach beginners

[@skipbrewer8101]

d easy one

[@SandraDevant]

Omg stop the extra talking its so hard to focus

[@krunoslavregvar477]

👍🍀✌️🍀👍

[@kennethwright870]

4*3=12

[@chrisdissanayake6979]

12

[@ericgofreed1651]

21 minutes to explain this question is beyond ridiculous

[@MrSummitville]

Get used to it ...

[@OkkieTrooi]

🥱😴💤

[@stevencraven4897]

D

[@johnjacobjinglehimerschmid3555]

I think that explanation was waaay to long. Could have taken 10 minutes off ....

[@albertagblexor3204]

Your class is very boring too much talk

[@marcobsomer5574]

5 secondes

[@TheDarryl37]

Too much talking. Get on with solving the problem

[@petersearls4443]

Damnit STOPPPPPPPP. you get caught up in minutiae and screw everything up. Just show us how to do the exercise then go into the minutiae.

[@josephlaura7387]

d) 12

[@jald910]

12

[@Victory1950]

D

[@shakirhamoodi5009]

d) 12

[@subasu478]

12

[@366Gli]

12

[@bushtherapy7655]

12

[@philsaspiezone]

12

[@pennstatefan]

12

[@jenniferpoh9998]

12

[@DhurataMyftiu-zr3uw]

12

[@rajeshvyas934]

12

[@NormanFarr]

12

[@NormanFarr]

12