SOLUTION: Hi! I need some step by step guidance on the following: (a^1/2b)^1/2(ab^1/2). I used the power of the product rule and arrived at: ((a^1/4b^1/2)(ab^1/2). I am lost at this point

Algebra ->  Square-cubic-other-roots -> SOLUTION: Hi! I need some step by step guidance on the following: (a^1/2b)^1/2(ab^1/2). I used the power of the product rule and arrived at: ((a^1/4b^1/2)(ab^1/2). I am lost at this point      Log On


   

Question 978039: Hi! I need some step by step guidance on the following: (a^1/2b)^1/2(ab^1/2). I used the power of the product rule and arrived at: ((a^1/4b^1/2)(ab^1/2). I am lost at this point. The rules are a bit confusing. Please and thank you. :)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Trying to figure what you are really starting with, my guess is this:

%28a%5E%281%2F2%29b%29%5E%281%2F2%29%28ab%5E%281%2F2%29%29, and you probably see two associated groupings.

%28a%5E%281%2F2%29b%5E%28%281%2F2%29%281%2F2%29%29%29%28ab%5E%281%2F2%29%29, and the rendering may not display very well.

%28a%5E%281%2F2%29b%5E%281%2F4%29%29%28ab%5E%281%2F2%29%29

a%5E%281%2F2%29b%5E%281%2F4%29ab%5E%281%2F2%29
and now you can use commutative property

a%5E%281%2F2%29%2Aa%2Ab%5E%281%2F4%29%2Ab%5E%281%2F2%29


Rule for exponents,
highlight%28a%5E%283%2F2%29b%5E%283%2F4%29%29

That still might be displaying poorly, so in pure text,
a^(3/2)b^(3/4)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hi! I need some step by step guidance on the following: (a^1/2b)^1/2(ab^1/2). I used the power of the product rule and arrived at: ((a^1/4b^1/2)(ab^1/2). I am lost at this point. The rules are a bit confusing. Please and thank you. :)
Continue by multiplying a1/4 by a, and b1/2 by b1/2 to get the simplified form: highlight_green%28highlight_green%28%28a%5E%285%2F4%29b%29%29%29