George T. | George T.--"It's All About Math!"George T.--"It's All About Math!"

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Amanda

Its a little difficult deciphering your notation, but assuming the expression is
(a^{1/2}b)^{1/2}ab^{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^{1/4}b^{1/2}ab^{1/2}

Next reorder to bring "like" variables together: a^{1/4}ab^{1/2}b^{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^{5/4}b