Cube root of (27a to the 8th times b cubed / 125 a squared) =? Many will GET WRONG!!

How to simplify radical expressions and cube roots using rational exponents.

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[devonwilson]

Greetings. The answer is 3a^2b/5. First, we will divide a^2 into a^8 to get a^6 which is equal to a^3 ×a^3 in the numerator. consequently, we are
left with cube root of(3^3a^6×b^3) divided by the cube root of 5^3=
3a^2b/5. Lovely.

[allystrya]

Problem = Cubed root of 27 a^8 b / 125 a^2

= Cubed root of 27a^6 b^3 / 125  
(when dividing the same number with an exponent; subtract the smallest exponent from both top and bottom which cancels out the smaller since x^0 =1. In this case a^(8-2) / a^(2-2) = a^6 / a^0 = a^6 / 1. And 125 * 1 = 125)

= 27 a^2 b / 125
(When “rooting” a “power” divide the power by the root. In this case a^(6 / 3) = a^2 and b^(3 / 3) =b^1 and since any number to the (^1) is itself b^1 =b)

= 3 a^2 b / 5
(Find the lowest number each whole number can be multiplied by 3 times. In this case 27 = 3*3*3 and 125 = 5*5*5)

[mingkee]

There's one little process to be done first
Get rid of a² >>> a⁸/a²=a⁶
Now you can process the whole thing
³√(27*a⁶*b³)/125
Then get root of power of 3
³√27=3
³√a⁶=a²
³√b³=b
³√125=5
Answer: 3*a²b/5

[padraicbrown]

Got it after a slight hiccup dividing the a powers!

Another nice challenge!

[alexredmonjr]

3a^2b/5 That's a good / fun problem.

[oldschoollew]

one step.... [3(a)^2(b)] /5 ... and was correct took me longer to write it down lol .... edit This problem contains a redundancy as well to confuse it

[MathsMadeSimple]

Tablet class math the type of guy to solve math problems while brushing guys teeth

[GLGS]

I don't see how changing the Cube Root to a 1/3 power helps with anything at all - after dealing with the a^2 you can just take the cube root of all Numerator and Demoninator.

[grahamwilliams]

Even more of us don't want to know what to do!😂

[catwoman]

(3a^2)b/5 disclaimer: I did not do this math problem, my Math Major son did. Lol...

[mrsandmom]

I definitely did not know what to do, but I understood the teaching and understood the answer

[pghphred]

You said 2 times 6, when actually it’s multiplying two 6 times.

[paulelliott]

are you under the impression that youtube pays by the number of words you