cube root of 24 x^3 y^8?

Question

how do I do this?

Answer 1

2xy^2(3y^2)^(1/3)

divide the exponents by three, leave the remainder in the root.
find the lowest cubic factor in 24 (8=2^3) and take it out, leave the 3 in.

Answer 2

Take the cube root of each of the three terms in the product given in the problem. This gives 24^(1/3) * (x^3)^(1/3) * (y^8)^(1/3).

Exponents of exponents can be simplified as one exponent whose value is the product of the individual exponents. This simplifies to 24^(1/3) * x * y^(8/3).

Answer 3

whenever you have a combination of numbers and variables being multiplied (MULTIPLIED ONLY) you can think of them individually and then put the answers together at the end...so let's break it apart.

with cube root you ask yourself "what's being multiplied 3 times?" Whenever you have 3 identical numbers or variables being multiplied (think third power), you can "bring that object out of the root" and leave the rest inside.

let's just go left to right...croot 24. First factor it.
24=2*2*2*3. Now I notice that 2 is being multiplied 3 times, so 2 comes out and the 3 stays inside. (NOTE...just 2 comes out, NOT 2^3)

next the x^3...it's probably the easiest...x*x*x...x three times, so x comes out of the root

finally the y^8...I recommend writing this all out the first couple times you do it, or as long as it takes for you to see how this works...
y*y*y*y*y*y*y*y= (y*y)*(y*y)*(y*y)*(y*y) - I just paired them
Note that I have y^2 * y^2 * y^2 * y^2...I have three y^2 and one left over, so y^2 "comes out of the root" and one y^2 stays in.

I know it's ugly, but this is tough over the internet...Now you put it all together.

So I have 2*croot(3) * x * y^2 * croot(y^2). Now put those not in a root together at the front and all of those in the cube root together inside the root to get....

2xy^2 croot(3y^2).

Answer 4

^(1/3) means cube root
^2 means squared, ^3 - cubed

24=3*8=3*2^3, so 24^(1/3)=2*3^(1/3)
cube root of x^3 is just x
(y^8)^(1/3)=y^(8/3) = y^2*(y^2)^(1/3)

Answer 5

when mulitplying under a root sign you can take the multiple of severas root signs so:
Cuberoot(24 x^3 y^8) = Cuberoot(24) X Cuberoot(x^3) X Cuberoot(y^8)
The answer should be:
2X Cuberoot(3) X x X y^(8/3)

Answer 6

fifty 4 = 2 * 3^3 sixteen = 2^4 = 2* 2^3 24 = 3 * 2^3 so fifty 4^(a million/3) = 3 * 2^(a million/3) sixteen^(a million/3) = 2 * 2^(a million/3) 24^(a million/3) = 2 * 3^(a million/3) so subject = 3* 2^(a million/3) + 2* 2^(a million/3) - 2*3(a million/3) = (3 + 2)*2^(a million/3) - 2*3^(a million/3) = 5 * 2^(a million/3) - 2*3^(a million/3) or A)

Answer 7

ummm 2

Answer 8

2*cbrt3xy^2

Answer 9

cbrt(24x^3y^8)
cbrt(8x^3y^6 * 4y^2)
cbrt(8) * cbrt(x^3) * cbrt(y^6) * cbrt(4y^2)
2 * (x^3)^(1/3) * (y^6)^(1/3) * cbrt(4y^2)
2 * x^(3 * (1/3)) * y^(6 * (1/3)) * cbrt(4y^2)
2x^(3/3) * y^(6/3) * cbrt(4y^2)
2xy^2cbrt(4y^2)

ANS : (2xy^2)cbrt(4y^2)