Expert: Abe Mantell - 12/25/2007

Question
Simplify the radical:.   �ã63xy11 /�ã7xy
Assume that all variables represent positive numbers.

The problem is: square root-63xy to 11 power divided by square root 7xy.

Answer
Hello Marcia,

I am not sure I understand...let me rephrrase it and
tell me if it is what you mean.  I will use the following
(standard) notation:
sqrt(A) = square root of 'a'
a^n = 'a' raised to the power of 'n'
a*b = 'a' times 'b'

So, did you mean:
{[sqrt(63xy)]^11}/sqrt(7xy)?

If so, then it simplifies as:
{[sqrt(9*7xy)]^11}/sqrt(7xy)
={3[sqrt(7xy)]^11}/sqrt(7xy)
=3[(7xy)^(11/2)]/(7xy)^(1/2), since sqrt(a)=a^(1/2)
=3(7xy)^(11/2 - 1/2)=3(7xy)^(10/2)
=3(7xy)^5
=3(7^5)*x^5*y^5
=50421*x^5*y^5

OK???

Happy Holidays!  :-)

Abe