SOLUTION: Can someone please help me Simplify or reduce these Radicals {{{root(3,24x^5y^3)}}} Please help me I do Appreciate it

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Question 196224: Can someone please help me Simplify or reduce these Radicals
root%283%2C24x%5E5y%5E3%29
Please help me I do Appreciate it
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What you have is the cube root of 24x%5E5%2Ay%5E3
If I say a%2Aa%2Aa+=+24x%5E5%2Ay%5E3, then
a+=+%2824x%5E5%2Ay%5E3%29%5E%281%2F3%29
I can also say


%2824x%5E5%2Ay%5E3%29%5E%281%2F3%29+=+3%5E%281%2F3%29%2Ax%5E%285%2F3%29%2A2y
%2824x%5E5%2Ay%5E3%29%5E%281%2F3%29+=+%283x%5E5%29%5E%281%2F3%29%2A2y

Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

Note: Josmiceli's solution is not acceptable for this is not supposed to be done by fractional exponents!
Edwin's solution:

root%283%2C24x%5E5y%5E3%29

Break 24 down into prime factors:

24+=+2%2A2%2A2%2A3

Break x%5E5 down into prime factors:

x%5E5+=+x%2Ax%2Ax%2Ax%2Ax

Break y%5E3 down into prime factors:

y%5E3=y%2Ay%2Ay

Substituting:

root%283%2C24x%5E5y%5E3%29

root%283%2C2%2A2%2A2%2A3%2Ax%2Ax%2Ax%2Ax%2Ax%2Ay%2Ay%2Ay%29

Since the index is 3, use parentheses to
group as many groups of three like factors
as possible under the radical:

root%283%2C%282%2A2%2A2%29%2A3%2A%28x%2Ax%2Ax%29%2Ax%2Ax%2A%28y%2Ay%2Ay%29%29

Write each group of three as a cube:

root%283%2C%282%5E3%29%2A3%2A%28x%5E3%29%2Ax%2Ax%2A%28y%5E3%29%29

Take the cube roots of those cubes outside
in front of the radical.  Leave the factors
that did not group under the radical:

2%2Ax%2Ay%2Aroot%283%2C3%2Ax%2Ax%29

Write the x%2Ax as x%5E2 under the
radical:

2%2Ax%2Ay%2Aroot%283%2C3%2Ax%5E2%29

2xy%2Aroot%283%2C3x%5E2%29

Edwin