Cube root of (27a to the 8th power times b cubed / 125 a squared) =? BASIC ALGEBRA!

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[historyworldofarjun]

First of all you simply take out 3/5 (³√127/25), --(i)
then using law of exponents : a⁸ - a² = a⁶,
then we have ³√a⁶b³,
now using law of exponents we have :-
a⁶ * ⅓ = a²; b³ * ⅓ = b; -(ii)
So combining (i) & (ii),
We get:- 3a²b/5

Important Concept :
If a surd is given in the form :
xth root of y to the power z;
ie, x√y^z; then we have;
--> y^z/x. By applying this formula, this question can be solved.

Thanks for staying till the end 😊, like 👍🏻, if you find it helpful !! 📗👨🏻‍🏫✍🏻

[adrianm.]

Wow, watching your videos is working so much is coming back. I got this one right before I watched this video, I wouldn't have remembered how a few weeks ago. Thanks for helping revive a 71 year old brain.

[MargaretCutt-umiq]

oh my gosh, i figured it out in my head! lol you have to understand, haven't done math like this in decades and watching these videos showed me i DID do math (decades ago) I was NOT good at it! thanks!

[martinwalker]

In college I was taking statistics. I sat outside the door of one section of statistics and understood the instructor better than the instructor for my section. I would have switched sections however I was working nights and had to drive 75 miles after work to college and I couldn’t guarantee getting to the first class in time.

[bigdog]

super simple as there is no addition or subtraction in the original problem.

Step one locate your perfect cubes. they are 27, the Variable B and 125. The cube root of 27 is 3, the cube root of the variable b^3 is just b. and the cube root of 125 is 5.

Step 2 reduce the a variable through subtraction. This leaves us with the variable a^6.

Step 3 Now for the hard part. a^6 isn't a perfect cube, but it can be evenly divided by the root which is 3. So 6 divided by 3 is 2. This leaves us with a^2.

Final step. no roots are left in the numerator or denominator, so final answer is (3a²b) / 5

[clmkc]

What looked like a hard problem becomes relatively easy if we know the proper steps and methodology. I like the basketball analogy!

[Shay-qu]

Numerator:
27 is 3 * 3 * 3, a is a ^ (3 + 5), and finally b is b * b * b
New numerator
3ab(a^5/3)

Denominator:
125 is 5 * 5 * 5
New denominator
5(a^2/3)

New Problem:
[3ab(a^5/3)] / [5(a^2/3)]

we have a to the 5/3 power in the numerator and a to the 2/3 power in the denominator
(a^x) / (a ^ y) is the same as a ^ (x- y) this leaves us with the cubed root of a cubed which is just a.

Final answer:
(3a²b)/5

Super simple indeed.

[NWSCS]

Knowing what to look for and how to break this down is the key. 27 is a perfect cube. Then we separate out a sixth power of a and b cubed. This leaves an a squared term in the numerator which cancels off with the a squared term in the denominator. 125 is a perfect cube as well. After all is said and done we end up with 3a^3b/5 as the final answer. This can be solved by simply knowing what are perfect cubes or the exponents that are divisible by 3 and understanding fractional exponents.

[jsand]

Many won't even try. But after seeing the answer it all made sense.

[laurendoe]

I prefer to write constants grouped together followed by variables. If I was writing it on paper, I would write three fifths then a²b

[redbeard]

In my head... reduce the variables to a6b3. Cube root is a2b. 27 root is 3; 125 root is 5. So (3/5 )a2b. In like 10 secs.

[Phoenix]

I did it in my head in about half a minute

[Steven-vl]

how can you possibly take 15:06 to solve this problem ... 5 seconds in my head (3/5)*a^2*b

[huntergatherer]

God you made heavy work of that. Talk about overcomplicating that

[Astriema-lrwo]

Many will get wrong? Maybe like one person...

[harrymatabal]

Margaret better than John who knows no maths

[henkhu]

see 8:59
So the the cube root of 27 is 27 ? That's what you write!
Please stop teaching this kind of mathematical nonsense. We have seen enough of it in your videos.

[soniyaSharma-licz]

It's a 9th grade question for Indian students 😂

[kimberlyshelton]

I don't how why it took so long to explain that. That's why kids are so confused.

[ernestscarrizales]

LOL and what is the everyday application of this problem.