simplify (a^(1/2)b)^(1/2)(ab^(1/2))

Question

Please help me figure out how to simplify the above 

Answer 1

 

Amanda

 

Its a little difficult deciphering your notation, but assuming the expression is (a^1/2b)^1/2ab^1/2, you can simplify as follows:

 

First distribute the exponent to the upper right of the first parenthesis (1/2), by raising each term inside to the power shown of 1/2.  Note that when raising a variable with an existing exponent to another exponent, the exponents should be multiplied.  So a^{1/2 raised to 1/2} equals a ^1/2*1/2 or a^1/4.  The resulting expression is as follows:  a^1/4b^1/2ab^1/2

 

Next reorder to bring "like" variables together:  a^1/4ab^1/2b^1/2

 

Finally complete the multiplication of "like" variables by adding the exponents:  a^(1/4+1)b^(1/2+1/2)

 

Since 1/4 + 1=4/4+1/4=5/4 and 1/2+1/2=1, the final result is a^5/4b

 

Hope this helps!!