SOLUTION: {{{(3(81a^5b^10)^(1/3))/((3b^4)^(1/3)))}}} can someone walk me through this Please?

Was the problem given as a quotient of two  powers,
like this:?

 

or was it given equivalently as a quotient of two cube roots, 
like this:?



Regardless, consider it as in the above form.
Separate the 3 coefficient of the numerator out in front as a 
coefficient of the entire fraction:



A quotient of cube roots can be written as the cube root of
a quotient:



Under the cube root, we divide the 3 on the bottom into the
81 in the top, getting 27, and we divide the b4 in the
bottom into the b10 on top by subtracting exponents
getting b6.  and we have this:



We know the cube root of 27 is 3 so we can take the 27 out of the
cube root radical and put a 3 in front of the cube root radical.
We can also take the cube root of b6 by dividing the exponent
6 by the index of the radical 3, getting b2 in front of
the radical.  So we have


  
We can multiple the 3's in front getting 9 and eliminate the
parentheses:



We haven't finished because we have an exponent 5 under a radical
that is larger than the index of the radical, 3, since it is a cube
root.  So we write the exponent 5 in terms of the largest possible
multiple of the radical index, 3.  The largest multiple of 3 that
does not exceed 5 is 3 itself.  Therefore we write the 5 exponent
as 3+2:



Then we remember the rule for adding exponents when we multiply
in reverse and change a3+2 to a³a²:



Finally we can take the cube root of a³ out on front of the radical
as just "a" and our final answer is:



Edwin