Question

How do I simply (a^1/2b)^1/2(ab^1/2)

Answer 1

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 a1/2 raised to 1/2 equals a 1/2*1/2 or a1/4. The resulting expression is as follows: a1/4b1/2ab1/2

Next reorder to bring "like" variables together: a1/4ab1/2b1/2

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 a5/4b

Hope this helps!!