`((4^(-3/2)x^(2/3)y^(-7/4))/(2^(3/2)x^(-1/3)y^(3/4)))^(2/3)`

Don't panic when you see this one!

In the first step, we move the top expressions with negative exponents to the bottom, and the bottom ones with negative exponents to the top.

`=((x^(2/3)x^(1/3))/(2^(3/2)4^(3/2)y^(3/4)y^(7/4)))^(2/3)`

Then we multiply terms with the same base (the x and y terms), by adding their indices. We can collect the `2` and `4` because they both have power `3/2`.

`=((x^(2/3+1/3))/((2xx4)^(3/2)y^(3/4+7/4)))^(2/3)`

Next, we raise everything to the power `2/3`, since that was the power outside the bracket.

`=(x/(8^(3/2)y^(10/4)))^(2/3)`

The final step is to tidy up the expression.

`=x^(2/3)/(8^((3/2xx2/3))y^((10/4xx2/3)))`

`=x^(2/3)/(8y^(5/3))`

Whew!

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