SOLUTION: Please help me to evaluate this problem (x^(1/6)x^(-3/4))^-2 x^(3/2) ^=raised to

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Question 276748: Please help me to evaluate this problem
(x^(1/6)x^(-3/4))^-2 x^(3/2)
^=raised to
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E%281%2F6%29x%5E%28-3%2F4%29%29%5E%28-2%29%2Ax%5E%283%2F2%29
The natural place to start is inside the parentheses. But to multiply in the parentheses, the rule for the exponents is to add the exponents. While there is nothing wrong with doing this, I am going to postpone this (since the exponents are fractions with different denominators) in the hope that it will get easier later on in the problem. Instead I am going to use the property, %28ab%29%5Eq+=+a%5Eq%2Ab%5Eq to raise the expression in the parentheses to the -2 power:
%28x%5E%28-1%2F3%29x%5E%283%2F2%29%29%2Ax%5E%283%2F2%29
Now it is time to start adding exponents. The two on the right already have the same denominator so I'll start by adding them:
x%5E%28-1%2F3%29x%5E3
Now to add -1/3 and 3:
x%5E%28-1%2F3%29x%5E%289%2F3%29
x%5E%288%2F3%29