64 to the 3rd power divided by 8 to the fourth power =? All You Need Is BASIC MATH!

[@brucea9871]

I started this just to leave a comment. I can't believe this video is 15 minutes; I figured this out in my head in seconds. 64 = 2^6 so 64^3 = (2^6)^3 = 2^18 (by multiplying exponents). 8 = 2^3 so 8^4 = (2^3)^4 = 2^12 (again by multiplying exponents). So 64^3 ÷ 8^4 = 2^18 ÷ 2^12 = 2^6 (by subtracting exponents) = 64. That doesn't take 15 minutes.

[@bongo_d2158]

Not every one is as "BRIGHT/BRILLIANT " as you are...😮😊

[@jald910]

8^2 =64 so 8^4 =64^2. So problem becomes 64^3/64^2 =64.

[@BrenoStrato]

(8²)³ / 8⁴ 8⁶ / 8⁴ 8² = 64.

[@johnshaw6702]

Why he used 2 instead of 8 for that explanation is beyond me. If he wanted to use 2, then he should have did it after 8 to drive the point home.

[@BlackhawkPilot]

Easy to solve in your head this way! Just solve the exponents. 2+2+2-4+2 there fore the exponent of 8 is 8 and 8 to the 2d power is 64.

[@generalgrafx]

This is the easiest way in my opinion.

[@BrenoStrato]

@@generalgrafx In Mathematics, it's interesting to synthetize and make solutions more elegant. The simpler and more direct, the better. 🙂

[@BrenoStrato]

@@johnshaw6702 We can even use base 2, but the solution becomes more complex and time-consuming, although the result is the same.

[@panlomito]

64 = 2^6 and 8 = 2^3 so (2^6)^3 . 2^(-3)^4 = 2^(18-12) = 2^6 = 64

[@obiku1971]

64^3 : 8^4 = 64^2×64 : 8^4 = (8^2)^2 × 64 : 8^4 = 8^4 × 64 : 8^4 = 64 Or 64^3 : 8^4 = 64^2 × 64 : 8^4 = 64^2 × 64 : (8^2)^2 = 64^2 × 64 : 64^2 = 64

[@italianviking80]

I took a slightly unconventional approach. I know that when dividing exponents with the same base, you simply subtract the exponents. To express 64³ in terms of 8, I recognized that the square root of 64 is 8. Therefore, 64 is equivalent to 8². This allows us to rewrite 64³ as (8²)³, which simplifies to 8⁶. From there, dividing 8⁶ by 8⁴ yields 8^(6-4) = 8² = 64.

[@gavindeane3670]

8⁴ is (8²)², and 8² is 64, so 8⁴ is 64². So we have 64³ / 64², which is just 64.

[@stevendebettencourt7651]

This seems ridiculous. How can you calculate this without a calculator!? Watch this. 64^3 / 8^4 Notice that: 64 = 8^2 So we can do a little substitution: 64^3 / 8^4 = (8^2)^3 / 8^4 Remember how exponents combine: (a^b)^c = a^(bc) So that means: (8^2)^3 / 8^4 = 8^(2*3) / 8^4 = 8^6 / 8^4 Another rule about how exponents combine: a^b / a^c = a^(b-c) Applying this: 8^6 / 8^4 = 8^(6-4) = 8^2 = 64 Now that I think about it, there’s a faster way to do this, watch: 64^3 / 8^4 Remember this: Everyone knows that 1+1=2, but I KNOW 2=1+1. In this case, we know 4=2*2. So, 64^3 / 8^4 = 64^3 / 8^(2*2) Recall: a^(bc) = (a^b)^c Thus: 64^3 / 8^(2*2) = 64^3 / (8^2)^2 = 64^3 / 64^2 And then: a^b / a^c = a^(b-c) So: 64^3 / 64^2 = 64^(3-2) = 64^1 = 64 There you go.

[@Coolpro99]

That makes sense now I can see clearly on this 😊

[@charlesheit4880]

DUDE! You lost me halfway through your explanation! So much for it being easier.

[@stevendebettencourt7651]

@@charlesheit4880 Where did you get lost? Maybe I can be a bit clearer.

[@juergenilse3259]

You don't need the rule a^n/a^m=a^(n-m), if you rewrite 64^3 to 64*64^2 (the recirsive definition of the power with whole numbers as exponent is a^0=1 and a^(n+1)=a*a^n which can be used for the rewrite), because then the 64^2 in the enumerator will cancel the denominator ...

[@juergenilse3259]

@@charlesheit4880 "halfway through his explanation" is a complete explanation, since he provided 2 different explanations ...

[@bravewave2084]

I wrote it out 64x64x64÷8x8x8x8. I expanded each 64=8x8. Then I wrote it like a fraction and used brain magic with Identity Properties and viola! 64.

[@aqraazie7698]

Your method of solving this problem is as complex as touching your ear from behind your neck. Do it in a easy way if possible.

[@phileakins1407]

I'm obviously watching too many of your videos! I went straight to the second method. Thanks, John; what you are teaching must be sinking in.

[@abdicatedprince1149]

Well. 64 is 8 x 8. (8x8) (8x8) (8x8) / (8x 8 x 8 x8) . You'd be left with 1 (8x8). , which is 64. Or you could just say 64^3 /64^2, that's 64^ (3-2) or 64.

[@George50809]

I used method two, powers of 2, and solved it in my head.

[@jimmypockrus7725]

64 262144÷4096=64.

[@TiaksengTe]

64 raise to 3is equal to 8 raise to 6 divided by 8 raise 4. The answer is 8 raised to 2 which is 64.

[@johnshaw6702]

8^4 = 8^2 * 8^2 = 64 * 64 64^3 ÷ 64^2 = 64

[@terry_willis]

First thing tomorrow morning, I'm heading to the local tattoo parlor and have "PEMDAS" tattooed on the inside of my eyelids.

[@hmerki]

:) haha In Croatia nobody use or talk about PEMDAS. We just know it.

[@JasonKing-m6m]

I took a short cut and used a calculator = 64....

[@twentyrothmans7308]

Thank you! I used method 2 because it's more robust.

[@hmerki]

It's easy. 64^3/8^4=(8^2)^3/(8^2)^2=(8^2)^(3-2)=(8^2)^1=8^2=64

[@johnmarchington3146]

64³ = 64 x 64 x 64, which is equal to 8 x 8 x 8 x 8 x 8 x 8. When that is divided by 8 x 8 x 8 x 8, the result is 8 x 8 or 64.

[@Stylux-z1p]

rules : (a³)² = a^(3x2) = a^6 a³ : a² = a^(3 - 2) = a 64³ = (8²)³ = 8^6 8^6 : 8^4 = 8^(6 - 4) = 8²✅ ------------------------------------------------- 64³ = 64 x 64 x 64 8 x 8 x 8 x 8 x 8 x 8 = 8^6 8 x 8 x 8 x 8 = 8^4 64 x (64 x 64) / (64 x 64) = 64 = 8² (64 x 64 ) numerator/denominator will cancel out

[@thenetsurferboy]

I did this mentally in under 5 seconds Simply [8 to power 6] / [8 to power 4] = 8 squared = 64

[@raya.pawley3563]

Thank you

[@thomas-gw3xf]

the answer is 8

[@juergenilse3259]

@@thomas-gw3xf Why do you think that, while everyone else got the result 64???

[@bazkeen]

Pretty straightforward 👌🏻👌🏻 =64³/64² = 64

[@EricWells-s2p]

PEMDAS is a mnemonic (memory aid). PEMDAS is NOT an acronym.

[@Alfredo-uc9dx]

GREAT,

[@BretFromPhilly]

IMH 64^3/64^2

[@danielmadden9691]

64^3=8^3×8^3/8^4=8^6/8^4=8^2 which equals 64 so 64 is the answer

[@giannaleoci2328]

8^6:8^4= 8^2=64

[@rbpeirce]

I stopped early in the video. Here's the easiest way I could think of. 64^3 / 8^4 = 64^3 / 64^2 =64

[@hmerki]

Or even better 8×8×8×8×8×8/8×8×8×8=8x8=64

[@mrmalco11]

How about just changing the 64 to the third power to 8 to the 6th power now you have the same base (8) so 8 to the 6th divided by 8 to the 4th is 8 to the 2nd =64

[@gavindeane3670]

Or change 8⁴ into 64² and then you have everything with the same base of 64.

[@juergenilse3259]

64^3/8^4= 64*64^2/8^(2*2)= 64*64^2/(8^2)^2= 64*64^2/64^2= 64 5 lines for the solution. Now i will look, how many lines will be necessary for the solution in the video ...

[@RRRSSS1111]

64

[@jamesblack702]

24

[@don911donny9]

64^3 is (8^2)^3, this gets based the same. (8^2)^3 is 8^6, this divided by 8^4 is 8^2 which is 64 (I couldn’t use the equals sign in this message as my phone kept working out the answers…!!)😅

[@ruperttristanblythe7512]

Wish you would just solve the problem. Pedmas should be another video. Had to listen to that, then adverts, then you advertising your channel. Too many interruptions if trying to concentrate. Lose focus and interest on the initial problem

[@EricWells-s2p]

64 to the third power does NOT mean to multiply 64 by itself four times. Please STOP sabotaging your students' learning!

[@davidhair8295]

I think the answer is 1.

[@TinWinU]

512

[@josephlaura7387]

64

[@LarryG-c6i]

64

[@generalmanagerformays587]

64

[@billmorris2613]

64

[@ollitrop46]

64

[@AC34D]

64

[@randallheisey3698]

64

[@rogerhart1835]

64

[@rodfulford4306]

64