SOLUTION: I am practicing for an algebra college exam. The question asks me to divide and simplify this expression: 1 2 (((a^3 b^4)/(6 b^3))^.5)/(((a^3)/(2

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Question 316225: I am practicing for an algebra college exam. The question asks me to divide and simplify this expression:
1 2
(((a^3 b^4)/(6 b^3))^.5)/(((a^3)/(24 a^2 b))^.5)
I understand that anything to the .5 is the same as square root. And I believe that the first part will be:
(((a^3 b)/(6))^.5) with the second part being:
(((a)/(24 b))^.5)
The problem I am having is simplifying it with the division between the two sides. I know I need to flip the second part; but I am confused as to how to do this with the radical. The answer is supposed to be 2ab , but I do not know how to get there. If you could help me, it would be much appreciated.
~hbanana
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You are quite correct in saying that your expression is equivalent to:

Now you can apply the following rule for radicals:

And write:

Now you can, remembering to keep everything under the radical for the moment, invert the denominator fraction and multiply:

Now multiply the fractions as you normally would:

Next, eliminate factors common to both numerator and denominator, to wit, the entire denominator:

Take the square root of the perfect square:

John